"Do you wonder what makes your child behave the way they do?"
Total nonsense, of course. Grammatically incorrect anyway you parse it.
"Do you wonder what makes your child behave the way he does?"
Grammatically correct, and traditionally understood that "he" is generically representative of either sex. Drives the feminists up the wall.
So, awkwardly, "behave the way she/he does?" I have actually seen this sort of thing.
Or, "behave the way it does?" Cold, man. A child is a person, after all.
"Do you wonder what makes your children behave the way they do?" Tada! Grammatically correct. But wait. Does this suggest that there is a herd of kids and all their behaviors are inexplicable?
Well, what's wrong with that?