:)
I firmly believe that the batfam would be a half-decent family to be adopted into while not knowing about their Nighttime Activities TM... at least in the beginning.
Lets say that Kiddo gets dropped off after the death of their last guardian (mother, most likely) and somehow the cops get their hands on a letter or something that says that Kiddo is Bruce Wayne's biological child. CPS wouldn't DNA test a child otherwise, but with some sort of evidence they may. Either way, something tells me that as soon as Bruce was notified of the possible child he would get the test done lol. While that processes the kid would end up in foster care (yikes! Gotham foster care is def rough af) whether Bruce is a foster father or not (that sounds like a problematic placement and he'd probably have to pull strings if he wanted to take care of them during this time). So, for 3-14 days an already traumatized, possibly orphaned child waits in limbo in a cesspool of a foster system. Trauma on top of trauma. And then the results come back and Yay! You've got a daddy!
So they pack up everything and go live with the People's Billionaire who they have definitely seen scandals of on the news before. Can you imagine the thoughts going through their head at the time? Are the other kids gonna bully me? Does he even want biological kids? Is he abusive? Neglectful? Pervy?? Does he really drink that damn much and fall in that many damn fountains?!?
And then they'd meet him and he'd be... stoic? And awkward and kind of cold? Which they could definitely take wrong (Bruce is emotionally inept, not malicious) and assume he hates them off the bat. They withdraw, straining themselves and the barely-there relationship more. The ink's still fresh on their adoption and they already want to leave.
Anyway, lets say things pick up. They meet Dick, the emotional center of the household, and then Jason, their caring (if abrasive) older brother, and so on. They start to find their place. Maybe they still struggle to warm up to Bruce or really feel like on of his kids, especially since everyone else seems so comfortable.
But Dick invites them to get ice cream and burgers and whatever else just as an excuse to spend time with them and make sure they're adjusting well (or enough to be expected). Jason teaches them to punch and how to finally get A's on the English assignments, and how to actually like their English assignments. He buys them fancy bookmarks and they pretend not to notice that he has the same one (they match!). Tim comes to them whenever he finds out a new fact he thinks they'll like and lets you pull coffees out of his hands without too much complaint after he's surpassed his daily limit (he only gives a grumble and an affectionate look) Cass teaches Kiddo all the best places to hide during hide-and-seek and pulls you into her side during movie nights. Cass makes sure you always have someone to eat with if them want it and brings back food whenever she's out. After some work, Damian even lets you help him train Titus!
But they still can't quite settle in because... where did everyone go at night?
If Kiddo's home situation before wasn't exactly ideal then they'd be a light sleeper, which is how they'd wake, and if not it's because they go down for a glass of water or something and see way too many bedroom doors open and beds empty on their way. Either way, after living with people for so long they'd catch on.
They notice that every single person in the household had been unaccounted for at some time. Every single one of their siblings plus both adults in the house were getting together every night to do something without them.
The realization was like a stone at the bottom of their stomach. And so, they start to pull away.
And everyone notices.
