I wish I was lucky enough to not need to care about money. The added income might be needed to help with the extra cost that month when he has the kids. None of us know and assuming the rental is bad is not very open-minded. If he was renting to a group of 18 year old prostitutes using a barter system, then I would assume the worst. This doesn't sound like that.
I have rented vacation places many times and never rooted through anyone's personal stuff. Just b/c someone is renting doesn't make them bad, dangerous or dishonest. There are many people on this site who rent and I do not think of anyone that I am aware of as seedy.
From what Pippi writes, her ah is behaving better to her and her kids. Now it could all be a colossal hoax and he does burn the house down, but until that happens, it is a positive thing to be cautiously optimistic. Not naive, but not assume the worst is inevitable. Prepare for the worst, hope for the best.
I hope that things work out. Pippi, are you staying with your mom again during their visit with dad or are you staying in Europe?