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.