I'm going to try and answer OP's question genuinely because, based on what I've personally seen on social media, there is a pattern to why these moments are viewed so differently. I think there are 3 reasons why these moments are treated with varying levels of severity and those reasons are: Context (before and after the action), Narrative Punishment, and their "Pattern of Behavior"
You've already laid out the difference in set-up between the moments.
For Vi, Powder had just set off a bomb that went off just as their family was about to escape and directly killed their brothers. Vi had just watched them all die in front of her and learned her little sister that she had told to stay home was responsible for it.
For Caitlyn, Vi had just stopped her from killing Jinx again and during the argument that ensued, Vi compared her to Jinx, the person who killed her mother.
What led up to both these moments isn't good, but one is objectively significantly more traumatizing and immediate. What Powder did, even though it was unintentional, led to a significantly worse situation (literal death, they cannot get those family members back) than what Vi did in "Finally got the name right". Due to this, people are going to be more understanding of an extreme emotional reaction. (And I'll be blunt, I do not believe anyone who claims they would react better in this situation.)
Their age is a factor. You point out that Powder is a child, then say that Vi is a teenager-- another child. A teenager is a child. Vi was around 15 when this happened (14-16 to be exact), that is a child, no matter how you look at it.
(Was it the way Vi should have reacted? No. Was what she did okay? No. She didn't react well and she did traumatize Powder, but framing this as child abuse and Vi as an abusive person for this emotional reaction in a terrible situation is disingenuous in my opinion. And framing Vi as anything other than a child, separating a teenager from a child and placing an inherent maturity and power to that position that a teenager simply doesn’t have, makes her out to be more of an adult in a way that the show is already critical of and places an unrealistic standard on a child on how they should react in a horribly traumatic situation.)
Caitlyn is 23-25 by this moment, based on the broad ages we were given by the writers, which is an adult, and an adult reacting out of emotion and hitting someone they care about is going to be scrutinized more heavily than a child, even if the severity of the situations were comparable, which in this context they're not. (I'm not saying this to be harsh on Caitlyn, I don't fall into the "Caitlyn is an abusive person" wagon. I don't believe that. That's not the reading I have when it comes to her character at all.)
Plus, their actions following the moment aren't the same either.
Caitlyn leaves Vi behind so she can go after Jinx without someone who will stop her getting in the way. Based on what we see in the show afterwards, she has no plans on seeking Vi out or reconnecting. (This is based on what we see in the show. I personally believe Caitlyn did want to reach out and reconnect, but pushed it down. But that's headcanon, not text.)
Vi realizes she's hurt Powder and walks away to cool down. She doesn't want to hurt her anymore or lash out again. The second she sees that Powder is in danger, she immediately tries to run back to protect her, but is stopped, knocked out, and imprisoned by Marcus. She then spends the next 7 years trying to get information about Powder and get back to her sister. The first thing she does when they reunite is explain what happened and apologize.
One of those is naturally going to be more positively viewed by the audience than the other.
Vi, based on context, was much younger, was in a much more emotionally devastating situation, shows significantly more onscreen remorse, and verbally apologizes.
Based on that, her action is going to be viewed through a more sympathetic lens than the context surrounding Caitlyn's action.
I’m not saying I think the severity of the action is equal. You’ve pointed out that Vi hitting Powder is a lot more violent and personal. That’s true but frequently the two actions are looked at through the base understanding of “they hit someone they loved” and then context is extrapolated from there and once it’s taken at that level (which inherently puts the two on even footing even if they aren’t “equal actions”) the context can and is often read as more sympathetic in its framing of one over the other.
This is what I think is ultimately the biggest one when it comes to why people are much harder on Caitlyn than they are Vi. Due to the way most people think of narratives and storytelling (based on conventional storytelling), most people believe that a bad action should lead to punishment within a story.
Within Arcane, Vi is punished significantly more for hitting Powder than Caitlyn is for hitting Vi.
I do want to clarify that when I say narratively punished, I don't mean this in a moral way. Arcane doesn't really punish characters based on the morality of their actions, for the most part. I mean this more in the way that a character suffers direct consequences or consequences tied tangentially to the action the viewer deems "negative", even if those consequences don't necessarily happen because the narrative finds it negative.
There's a lot more narratively that viewers can point to where Vi is "narratively punished" for hitting Powder. Vi suffers a lot in the series due to this action through outside forces and her own guilt and self-hatred.
Vi is thrown into jail as a child where she's beaten for years right after she hits Powder, when she gets out her relationship with her sister is in shambles due to the bitterness that has been built up because of her last action, she's told directly by Jinx that she "created Jinx" through that action, she is wracked with guilt over it and takes responsibility for all of Jinx's actions, and is ultimately left completely alone in the fallout of all of this.
The weight of this action echoes out through Vi's entire storyline. Her actions, suffering, and guilt are all deeply tied to this moment in a way that Caitlyn's aren't.
Jinx also lets out a lot more of her anger and bitterness towards Vi over this action (the entire tea party, the "...he didn't create Jinx. You did", etc) than Vi does towards Caitlyn.
Caitlyn does face consequences for her actions as the commander (I don't understand the people who say she doesn't), but not directly for hitting Vi, unless you count Vi not being around and Caitlyn losing her only true support, which a lot of viewers don't really seem to count.
Viewers are conditioned to want a more direct consequence for a negative action than that. I know I saw a lot of people who were mad that Vi didn't call Caitlyn out for it, take longer to forgive her, or show more distrust towards her due to it.
Narrative punishment or what people view as narrative punishment, is a large part of why people are much more upset when it comes to Caitlyn's actions than they are Vi's, based on what I've seen.
If you've seen something different, then I guess we're on different corners of the internet.
3. Their "Pattern of Behavior"
I'm going to start by looking at their individual behavior towards the character they hit within the act the action happened, which influences people's view of the character and their action, even if this is meant to be contextualized as outside their normal behavior.
Vi's actions are a lot simpler because, for the most part, Vi is very supportive and gentle with Powder and consistently stands up for her in Act 1. We don't really get any indication that this is recurring behavior and Amanda Overton has specifically stated that "The Base Violence Necessary for Change" is the only time that kind of thing has happened and they didn't have an abusive sibling relationship.
Most other instances where we see Vi with people she cares about in season 1, she's explicitly framed as gentle and is frequently very affectionate. There isn't a pattern of abusive or violent behavior from Vi shown to us on screen within the show.
The music video is complicated because it wasn't directed or written by any of the writers or showrunners of Arcane, so while I could see a teenager/kid reacting out of anger due to the stress of the dangerous situation they live in and the pressure of their parental role, using it for context within the series doesn't fully work, especially when it's contradicted by the writers themselves.
There's also a very clear contradiction, other than what the writers have said, between the music video and the show, which makes its validity as an extension of the story very shaky. In the music video, we see Deckard and his group hanging out with Vi and her siblings while Vi teaches them to fight, but in act 1 it's made clear through dialogue that Vi doesn't know Deckard. ("Some idiot was following us." and "Tell strangers on the street that we got a nice haul?" - both in reference to Deckard and his group)
The music video is also a piece of media that many people who have watched the show likely haven't seen. So it's not going to factor into many people's opinions and interpretations of Vi as a character.
You are free to take this into account if you want. I'm more stating that many people who watch the series likely haven't seen the music video and that none of the writers/showrunners were directly involved and it led to blatant contradictions between the two, so this point won't influence as many people's view of the character in the same way as it might others and in some ways shouldn't based on the fact that this moment could have been a point of divergence between the writers intent in the show and the animators intent in the music video. We don't know.
(I want to clarify that I'm not saying that I think this moment being canon is completely out of the realm of possibility. When a child is put under that kind of pressure and raised in an environment rife with violence, those kinds of behaviors and reactions are very plausible, even if they aren't born of malice and are instead rooted in worry and stress. I'm simply saying that using the music video to determine a pattern of behavior doesn't fully work and it's not part of the main show, so a lot of people reacting to these moments haven't seen it and never will.)
Caitlyn's actions in Act 1 leading up to this moment are a large reason why people are so critical of the moment she hit Vi (based on what I've seen). Caitlyn pushes the badge onto Vi, which, while not done to intentionally hurt Vi, is on some level seen by many to be a test of her "loyalty". Plus, it's an insensitive thing to ask, given she knows what Vi's history with enforcers is. Vi is constantly on eggshells around her and is afraid to directly push back against her actions due to guilt and fear of abandonment. And when Vi does push back against her, Caitlyn is mad and tries to hurt her through her words, "I keep telling myself you're different, but you're not. It's her blood in your veins." This is then followed by Vi throwing this statement back at her "Then why are you the one acting like her?" which leads to Caitlyn hitting Vi.
All of these piled on top of each other lead to a negative view of her as a character, especially in regards to her relationship with Vi. It's a very different framing than Vi's relationship with Powder.
Vi is also a character who has been abused by enforcers her entire life. When she was in prison, she was beaten by them regularly. Caitlyn is an enforcer. Caitlyn is a person with tangible systemic power over Vi through this role and her position as the Kiramman heir. This moment will always be taken in that context. It cannot be divorced from this context.
Vi trusted Caitlyn and believed she was different. She believed that she wasn't like those other enforcers, only for Caitlyn to gradually fall into acting more and more like them and finally hit her. Caitlyn breaks that trust and becomes an active participant in this system that has oppressed Vi and her people. These pieces of context are major factors in why people view this moment so critically.
I'm going to asterisk this with my own opinion because I don't want this to come across like I believe Caitlyn is an abusive character. This is clearly meant to be behavior out of the ordinary for her. Her actions are clouded by grief and the pressure of her situation. She's been thrown into being the head of her house and has a sudden massive amount of power and responsibility put onto her shoulders. Everything is meant to be crashing down around Caitlyn at this moment and she's crumbling under the pressure and becoming more radicalized as a result.
All of Act 1 is essentially a pressure cooker for Caitlyn. The longer the hunt for Jinx goes on, the more she's blinded by desperation because she is clinging to the idea that taking the shot and killing Jinx this time will rectify her mistake in the season 1 finale. Caitlyn blames herself for not taking the shot when she had it and as a result, Jinx was able to shoot her rocket and kill her mother. She blames herself for her mother's death and feels like killing Jinx is the only way to make it "right". And when Vi stops her again, she hits a breaking point.
This is meant to be outside the norm for her. Caitlyn was the most compassionate character in season 1 (even if she was very naive and privileged). Plus, by act 3 when she isn't blinded by revenge and grief anymore we see that she has at least in part returned to some semblance of her old compassionate self (we don't really get to see enough of it, which I think is a large part of why Caitlyn's action doesn't get viewed through a more forgiving "this was out of the ordinary" lens that Vi's action gets).
Also, even if Vi was trying to give Caitlyn a wake-up call after almost shooting at and traumatizing a child, comparing Caitlyn to her mother's killer was not what she should have said. Caitlyn being upset in that moment makes complete sense.
It doesn't mean you have to agree with the actions she took or that she hit Vi (I don't agree with this moment and I do think this was bad), but understanding the context is important to understanding the action. I think this context is two-fold. It helps understand why she reached this point and allows for people who are looking for nuance to understand that this isn't how Caitlyn would normally behave, but it also creates a pattern of behavior for people who don't want to look beyond the surface level to point to and claim she is abusive.
It's a case where the context of their behavior sheds a more positive light on one while it puts one in a more negative light. This immediate context (the act the action happens) colors people's perceptions of the action itself.
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This is just based on what I've seen from people on the internet. To be fair, while I tried to approach this as objective as I could, I am biased towards a more positive reading of Vi, and, while I don't hate Caitlyn the way a lot of people online do after season 2, I don't like her nearly as much as I like Vi.
I tried to find a balance between objective and subjective, but how successful I was is debatable. You might not agree with my reading of the characters and their actions, which is fine.
I'm also going to be honest, maybe it's the corner of the internet I've found myself on, but I've never personally seen Vi hitting Powder be called normal sibling behavior. It's not. But I also don't think it's a moment that is irredeemable or abusive in the "Vi is an abusive person" type of interpretation. Which is the interpretation I've run into far more often on social media. I think both interpretations are extreme ends that fail to take the full context of the moment and the character into account.
That's also how I feel about Caitlyn, if my write-up above didn't make that clear.
There are a lot of people, or maybe a very vocal minority, who approach their interpretation of characters from the most extreme angle they possibly can. These interpretations often fall into "this character can do no wrong" or "this character has done everything wrong", with little in between. Both of those are uninteresting and flatten the character, removing their complexity and relatability.
I don't know if this was helpful or if OP actually just wanted to complain about fandom (which is completely fair haha). I just thought what OP said was interesting and I thought I could shed some light on why the two moments are viewed differently.
