Keep your ear to the ground for indications of any move.
About those false accusations - don't try to make sense out of them, like how the call went for the first few minutes, or how he doesn't own a robe, or if the "authorities" have been notified. That sort of hand-wringing is useless, it is a complete fabrication that you are trying to make sense of, logic and reason are absent. Your Ex-wife has a gun, and has pointed it at Jim's head.
I have a friend from High School, he became a photographer taking school photos of kids, as a way to work during college. His first client was a daycare center located in Southern California, near his school (University of Second Choice). There was an accusation of molestation at that school, and he - who only went there 3 times to take pictures - was swept up in the investigation and spent years defending against his involvement.
The case is rather famous now, have you ever heard of the McMartin Preschool? Read the wiki article and see how a single accusation can destroy third-party lives - even for my friend, the school photographer.
Jim can't be around your daughter, your ex-wife has a gun pointed directly at his head.
Volenti non fit injuria