The most crucial element of the BatLantern relationship is that Hal has to have beef with at least one of the batkids- whether its genuine or more on the joking side, this man genuinely needs to Loathe A Child. Its a necessary element of his being in love with Bruce
Bruce and Hal start dating early and Dick has a sticker in his chart that says “Does Not Play Well With Others”? Fuck yea. Dick is screaming obscenities at him, Hal is screaming them right back. He has genuine fucking beef with an eight year old. “Hal, he’s eight.” “Yeah, and he’s about to learn how aerodynamic that makes him. Hey fuckhead wanna see the sun up close?” “I’d like to see you try, wannabe glow stick!” “Oh you little rat fuck-” “Hal-”
I can’t see Young Jason having problems with him but Adult Jason and Hal would genuinely draw each others blood. Hal is a Husband first and Step-Father second- he has no patience for Jason and his Red Hood vendetta and guns and anger. He understands where its coming from but he will not let Jason take his insecurities and unwarranted aggression out on him and Bruce, not a fucking chance. Until Jason takes off the mask and drops the guns, Hal is relentless and unflinching on that point.
Tim and Hal have a rivalry based exclusively on their jealousy of each others Allotted Time Spent With Bruce. Hal is coming home from a long space mission and all he wants is to have Bruce wash his hair and then fall into bed together and not emerge for the next week. But when he staggers in the door Tim has accidentally fallen asleep on Bruce’s lap and Bruce cannot move if one of his kids is on top of him so Hal just has to settle for a quick kiss and go wash his own hair. Bruce is making Tim breakfast in the kitchen and Hal comes up behind him and wraps his arms around his waist, kisses his neck and drags him away. Hal and Bruce are sitting on the couch being Cute and Tim rushes in, wedges himself between them and starts talking to Bruce about his day while kicking Hal back. Hal has resorted to locking Tim in Air Jail with his ring to get some alone time with Bruce, and Tim has resorted to outside sources to keeping Hal occupied. Or rope.
Hal and Damian honestly I can see them having Problems early on, but I think Damian is actually the first one of the kids to accept Hal. (if you saw my headcanon saying that Damian is the last one to accept Hal shhh no you didn't) Damian doesn't think he’s worthy of being with his Father and Hal thinks Damian is an arrogant little shit head. Dick and Hal vibes. He sticks out a foot to make Damian trip as he’s running past. Damian stabs him with the craft scissors when Bruce asks Hal to help him with a school project in a desperate effort of having Bonding Time. Its glorious
Hal and Duke are my favs. Duke is BatLantern’s love child and I will die on that hill. Duke is merciless and will not back down. Hal physically cannot stay away from a challenge. “You're so in love with him you look ridonkulous.” “Please never fucking breathe in my direction again.”
Hal and Steph have a petty rivalry and it gets Serious a total of one time because Steph refuses to accept that she does actually care for Bruce Like That and it pisses Hal off because then that means she has no rights to hate on him or have this rivalry with him in the first place because she’s not his kid and he only has this relationship with bruce’s kids- but then after the Serious Argument it goes back to being fun. Prank wars and petty bullshit. “Who filled my entire apartment with water and made it an aquarium?” “I wonder who.” “Hal I cannot fucking get to school.” “Damn. should've thought of that before you bedazzled my ring.” “You bastard-”
Hal and Cass have a one sided rivalry and by that I mean both of them think they're crazy. Hal thinks Cass would like to murder him and Cass think Hal hates her. Hal’s hanging out with Bruce and cuddling him and Cass just appears at the foot of the bed and Hal screams so loud the bats in the cave fly away and falls onto the floor before running away because clearly Cass wants to spend time with Bruce and who is he to get between them hahahaha- hes not that suicidal. Cass sees this and is like :( he hates me. Hal is just scared of her. But they get over it and its lovely. Cass gets two girl dads
Hal and Barbara are flinty eyed and don't have a rivalry they have genuine beef. Hal is doing a mission and all of a sudden the cameras that hes switched off are back on and now hes running for his life. Barbara is sitting in her living room reading a book and then suddenly shes two miles away without her wheelchair. Barbara hugs Bruce on his wedding day and mouths that she laced his piece of the wedding cake to Hal over his shoulder. Hal wraps a gag around her mouth with his ring during the “if anyone objects speak now or forever hold your peace” time comes.
Anyway. It's important Hal has Beef with at least one or all of the Batkids. Its just a part of being in a relationship with Bruce- he has to Loathe A Child.