Batlantern/Batfamily/GLC idea of mine but I think, when they get serious enough and talk about "meeting the family", Hal chooses to introduce to Bruce to the Lanterns of Earth (and some)
Because what is there of the Jordans are a graveyard kept cold by unsaid words and breathless farewells, and the other half had always preferred to keep out of "that" business (whether it's the gay part or the cape part, Hal's not sure, nor does he want to know)
Bruce takes this in stride. Despite knowing everyone Hal considered "family" already, he treats them as he would impressing them as much as he could, when he met them in Hal's small apartment for a family dinner.
John and Jo are just glad it's not worse (/j). Jessica and Simon are respectful, and know Bruce well enough to be confident. Kyle chooses to stfu because Batman doesn't know he's banging his son and he'd like to keep it that way (Bruce already knows). Guy is, well, Guy.
But none of them really have anything bad to say after the initial shock of learning that the poster children for office beef have gotten together. After all, Bruce is rich, good with kids, responsible, and most importantly of all, he makes Hal quiet - smiling, calm, and safe. That's all that matters
It has come to their attention that becoming the (un)official Mrs Wayne meant that Hal was now charged with the custody of 5 (?) stepchildren, who are all as mysterious and insane as their dad
The first to make an encounter with the Batfamily after Batlantern's publicity is Guy, for all the best and worse reasons
[gearing up in the Watchtower, Hal and Guy are going]
Guy being Guy: Damn you playing nanny for the big Bat now? thought you couldn't handle allat. good luck with his batshit crazy kids though!
Guy, jumping: Jesus- FUCK where did YOU come from!?
Hal: Cass. Batgirl. She's coming with us on this mission to learn about off-planet JL protocol. You got a problem with that?
Guy: No but... damn, she's tiny. How old is she? She looks like she's just 6 apples tall,or whatever tf Kyle says these days. Is the Bats feeding her?
Cass: My brothers say I'm 7 apples tall
Guy: Almost thought she couldn't speak there, what do you know.
Hal: Cass is selectively mute. Half trauma response, half preference. She's deaf on one ear so don't blast her there, will you?
Guy, former special ed teacher, known to be more understanding with young heroes, new recruits, and anyone he determines to be a kid:
Guy: I would die for you, Cass
Cass: [reads his body language for a second]
Cass: Oh okay! 😊 Yay!! 😁 [unlatches from Hal and hooks her arm on Guy's]
Guy, tearing up: This is the greatest honor of my life 🥹
Hal: ...Bruce is gonna fucking kill us both
[returning to the Batcave]
Bruce: Welcome back, what's- [takes a step back after seeing Cass perched on Guy Gardner's shoulders]
Cass, holding pretty space rocks, a large alien smoothie, and a shirt that says "I came to the Far Sector and all I got was this shirt": Dad, this big orange meanie is now my favorite uncle on Hal's side
Bruce: [gives Hal a look]
Hal, trying not to laugh/cry: It was this or Kilowog, and we can't exactly bring Kilowog to Cass' dance recitals, can we?
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