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I have a headcannon that Batman is The supportive father.
In the normal sense that he would support his kids in whatever path they choose (vigilante, doctor, anything that's not a straight up war criminal really), supports and funds all their hobbies and passions and after seeing how hesitant the first kid to come out to him was, had pride flags hanging in every corner of the batcave, made pride pins that were safe to wear with their vigilante uniforms and maybe even brings back rainbow batman for a day if any of his kids were having a really hard time.
But also, he absolutely refuses to critique/scold any of his kids in public/in front of others.
Dick skips school because a travelling circus is coming to Gotham and claims his absence is because of a family emergency? (He doesn't know how to explain to Bruce that yes it will hurt to see the performers but it would also feel like returning home. That even though he loves his life now he still missed being in the circus) When the school calls Bruce that night, Bruce lectures Dick on the importance of honesty and "next time just tell me you want to go to the circus chum, I'd have sorted it out. I hope u had fun kid and... if u want, only if u want, we could go to one together sometime? I heard there was a show in Bludhaven next week..." Then the next day Bruce drops Dick off at his class and walks into that school sobbing, blubbering about how his emotional support cat had died and it was a miracle Dick was able to return to school so soon.
Bruce gets called down to a fancy store because Jason, who was wearing his old clothes, got accused of shoplifting? Bruce is there in seconds lecturing the store owner about how disgusting it was to judge his son based on his clothes, until littleJay tugs on his shirt and whispers "I did it." After which he lectures the store owner for having the checkout at the wrong place in the store, that's why his precious boy got confused! (And in the meantime discreetly slips Jason a $200 bill) "Did you even ask my kid if he had the money or did u just assume huh? Oh you didn't ask? Well why don't you ask him now Mr.Prick?" and Jason gleefully shows him the bill. Then in the car ride back home Jason admits that he was trying to steal the pretty pen because he wanted to give Bruce a nice present for father's day but he didn't have enough saved up and Bruce lectures him on honesty, trust and "I don't need an expensive gift sweetheart. Having u with me, to celebrate father's day with and knowing that u wanted to do something nice for me is all I need. .. the second best gift would be if u would give me a private showing of ur big speech in your school play?" (And that's how the tradition of Jason performing some monologue from his current favourite play every father's day started)
And the lectures/scolding for his kids only happening in private carries over to their vigilante life too. Batman will point out any mistake made by JL, in front of the criminals they are currently in the process of apprehending. Reading any post mission report he wrote feels like being back at school and getting back an assignment covered in red ink.
Then the younger heroes start joining. Now, the batkids are trained well - they make fewer mistakes than most of the JL - but mistakes still happen.
More BatMimikyu with suits.
LEGO BATMAN TRANS BATMAN???
IN MY LEGO BATMAN
DCAU Batlantern... But Rainbow Batman and Hal Jordan celebrate Pride Month!
Batman Pride by Ismael Álvarez