Isn't Batman the genius detective member of the League? Feel like he should be asking the questions. Unless he has figured it out already and just humoring the rest of them.
Your point has merit but he’s also an orphan who in his personal life sponsors an orphanage and programs to help orphans make their way through life successfully.
And takes in kids who are orphans or have issues and gets them to focus on positive things in life, like discipline, goal setting, and putting yourself in perilous situations while in armored spandex.
The league are almost all quite competent as well. If Bruce needs to put some pieces together then he probably trusts most members of the league to at least get the information they need. It's moments like these that I love about DC heroes. When they show the importance of the people and not just beating up bad guys.
He's also right next to them. He can probably hear all of it, and would be able to ask additional questions later if needed. Pretty sure he can multitask enough to hand over a puzzle piece while eavesdropping on a conversation.
Batman probably can learn all he needs to about the parents by talking to their children. Anything else about them he probably doesn't need to be in their presence to learn about. His status as an orphan also probably makes it a lot easier to relate to the kids rather than the parents.
I don't like kids. They're messy, annoying, loud, etc. more often than not and as they're not mine, ew. Add to that one time when I had a lady loudly claim I was trying to hurt her kid when said kid walked up to me thinking I was my father (a school employee) and I really dislike (literally palms a little sweaty, waiting for someone to say I'm doing something) being near kids if my wife isn't around.
However, if a kid comes up to me and is all "hey someone's on the phone for you" and hands me a toy phone, I'm gonna answer it and be good to the kid. Friend of mine and I used to put on little concerts for the preschoolers while we waited for the school bus, too.
If someone who actively tries to not be around children can manage to be a decent person towards one for a little while then people who can't have no excuse.
Why would they be? Batman is a famous good guy even within the context of the comic.
(The parents might be worried because having the Justice League show up means that they're involved in something dangerous, but kids don't think like that.)
Look at Batman's face in that panel! He is very angry. His mouth is down turned. His eyebrows are furrowed. His eyes are dead. I get the impression if that piece doesn't fit, he's going to beat some justice into those children.