So I have this rambly analysis about Pink...
Well first of all remember that she's a defective diamond, wich can cause what I think is some emotional instability, like she does tantrums but can't really control those emotions. This is basically because she's kinda like a child, and also VERY immature.
But to explain more about her character I really wanna look out to the movie, because the Diamonds told our beloved Spinel that "you remind us so much to her" so imagine an Spinel that had all of her baggage AND that inability to control her emotions (like, even Spinel kinda had more control than what I imagine Pink would had).
Also talking about the diamonds, damn they really have some fault on how Pink became like that. For what we keep seeing Pink was only there to entertain them and whenever she asked for something else she were excluded because "she weren't a real diamond" wich was real but of course that will cause the kid some damage, specially if she's THIS emotional...
And then, after all of this exclusion, she didn't had anyone that could understand her. You see, she tought that maybe after being with some people like her (the other Rose Quartzes) she could get someone to talk with about her problems, but it wasn't like this. I really think the CG were there to help her, but they could never understand how she felt, that's why she were like "oh let's go after the diamonds" because she felt that actually THAT was her problem, and if they were gone maybe she could have been happier (I can totally see the parallels with teenagers that hate their parents, so I believe RQ was Pink's emo phase lol).
Also I think Steven's Pink powers are activated whenever he feels impotent, excluded or any of those emotions that I believe Pink had too.
And well no wonder that the first time he does get to see Pink was on one of those moments, where he could feel that impotence because Connie also felt like that with her mother.
Anywyas I may be missing some points about her character but damn poor Pink, just a misunderstood kid that had actually no one to talk, like now Steven has the other Rose Quartzes and Volleyball had Pearl but Pink... Pink never had anyone that could REALLY understand how she felt, I think that's maybe why she kept so many secrets from the others, because no one could really get how she felt.
I feel like her life were just one bad decision after another, and just her trying to taste how it was to belong anywhere, because the only time that she belonged was when she hide who she really was to everyone else.