I think Bruce’s kids seperate Batman and their dad in their heads. They know, logically, that they're the same person, but it's how they separate "work" from "home."
Jason can sock Batman in the jaw and not feel an ounce of regret, but he's mean to Bruce once and feels unbearably guilty about it for weeks afterwards until he apologizes.
Tim gives Batman the cold shoulder for a month straight for not trusting him enough to let him take on an important case, but Bruce asks him whether he'll come for Sunday dinner and he folds like a bad hand of cards.
Damian doesn't listen to Batman on patrols and rolls his eyes at the Batglare™️ and lectures, but Bruce’s voice raises an octave when scolding him and he devolves into full-on sobs immediately.
Dick practices selective remembering. Bruce and him were yelling at each other when he was younger? No, that was Batman yelling at him; Bruce was the one that apologized and begged him to come home.
Duke's the only normal one, but even then he's beginning to seperate them. Like, it wasn't Bruce that made him train until he could barely walk—that was Batman. Bruce was the one that helped him up after and apologized and tucked him into bed.
Damian slips up around Bruce and says "Batman's unreasonable and unnecessarily cruel."
Bruce is stunned like, "I didn't know you felt that way, Damian. We can alter your training to be less strenuous if you feel like it's too much-"
Damian gives him a surprised look, "I wasn't talking about you, Father. I was talking about Batman."
Bruce tests him for hallucinogens when him attempting to say he is Batman end with Damian on the verge of a panic attack. The bloodwork comes up clean. His other kids go into similar states of distress whenever he tries to bring it up, so he accepts it as something his kids just Do.
