Is there a way you can hide a gps tracking device in one of your children's bags when you send them off with their father? That way you can track their whereabouts and then drive there to see if you can find his car. Then you should go on family watchdog and see if there are any convicted sex offenders living by or at the address. You can also find out the names of his roommates by searching the address on Spokeo. Once you have their names, you can run background checks on them.
Eta: I'm sorry, I just re-read your op - I thought you didn't know his new address so that's why I suggested the gps. If I were you, I'd hide a VAR in one of the kids' bags. I know you don't want to involve the kids, but sadly they're already involved and you MUST protect them in any way you can. A VAR can give you a better idea about what's truly going on over there. The kids don't even have to know you planted. Just make sure you put it somewhere they won't even find/feel it.