I think the most hilarious thing would just be other heroes visiting the batcave before they knew Batman & Friends’ identities.
Like,
Oliver: “Holy shit this must cost a lot of money how do you guys pay for all this equipment?” Robin: “The government.” Oliver: “Wait, seriously?” Spoiler: “No, Bruce Wayne actually moonlights as Batman. Yes, the government. You don’t even know how easy it is to blackmail a few City Council members and a couple of senators.”
Or Barry
*Batgirl and Red Robin burst into the cave from the clock entrance in full costume* Red Hood: “Sorry Guys, false alarm it was just Barry.” Barry: “Where does that door lead to?” Batgirl: “Supply closet.” Barry: “you really expect me to believe that?” Red Hood: “its a damn supply closet.” Barry: “Well then what were they doing in a supply closet?” Red Hood: “They’re sixteen and hormonal. You figure it out.”
And when the “supply closet” has a kitchen
*Barbara rolls out of the elevator with a tray of sandwiches on her lap* Barbara: “Agent A said to make sure everyone eats.” Arthur: “Isn’t that a supply closet?” Barbara: “It’s a big supply closet.” Arthur: “With a kitchen?” Barbara: “Like I said, it’s big.”
And, of course the kids thing, and the cave part of their home, so Bruce is in DAD MODE
Diana: “These are your children?” Batman: “No. I don’t have kids.” Nightwing, running into the cave: “THE FLOOR IS LAVA!” *Batman jumps on an office chair.” Diana: *cocks an eyebrow* “Somehow I don’t believe you.” Batgirl: “Batman having children? Damn, they must live some pretty awful lives. Emotionally distant father, unrealistically high expectations placed on them, NO time for fun because everything is just train, fight, do detective work. Those poor bastards.” *Nightwing, Oracle, Batgirl, Red Robin, and Black Bat all nod solemnly in unison*
Or before they realize Red Hood was the second Robin, not realizing that the Batcave is still a second home to him:
Cyborg: “Red Hood, what are you doing here?” Red Hood: “Babysitting duty” Cyborg: “Seriously.” Red Hood: “Okay fine. Bats is away so I decided I’d take advantage of the supply closet and Agent A.” Cyborg: “Why should I trust you?” Red Hood: “Look, I know you’ve tried getting into the Batcomputer system without permission. You really think I’m gonna be able to do anything harmful here? Seriously, I just wanted some cheap but amazing Pad Thai and I know how to navigate the cave system and get to the Batcave, so I decided to mooch off of Batman. Let me mooch in peace.” Cyborg: “Fine but if anything happens, I will be able to tell Batman exactly who was here and when.” Red Hood: “Adios.”
2 seconds later, Robin gets out of the showers. “Okay, brat. Bruce says bedtime at 8 tonight cause you’re grounded but I made some fucking good pad Thai and I need validation so have some, tell me how good it is, and we won’t tell him you stayed up an hour late.”
Or a gem like this:
Oliver: “I found Red Hood in Star City. Thought you’d want him back here.” Red Hood, handcuffed: “Damn, is this the Batcave? Holy shit this is pretty awesome. Oh wow who’s costume is that? Oh fuck that’s the Robin that died, right? What happened to him, again? Wasn’t it the Riddler? No, no wait it…right the Joker. Damn, I’m sorry Batsy that’s really gotta suck. I can only imagine….” Batman: “…” *just walks away* Oliver: “Uh, B? Do you not want this nicely delivered package? At all?” Batman: “Thank you, Oliver. Please leave him here. You can go.”
(As soon as Oliver is gone, Jason puts his helmet up. “Okay, you gotta admit that was pretty funny.” Bruce turns around, cowl pulled down, trying not to smile: “Don’t disrespect my son like that again.”)