How do you treat confidential information innocently passed on by a child that could be damaging to the parent?

You have to deal with it on a case by case basis. If the kid tells you that his dad likes to walk around in ladies underwear then you probably are not going to go anywhere with that info. But if he tells you that dad is burning mom with cigarettes that is a cause for worry and a reason to call and share this information with Division of Family Services. They will handle it in a confidential manner. And yes, these are cases that I have dealt with.