Agree^^^^^. These are some dangerous warning signs and look at your great instincts in thinking something was wrong!
Seek advice from a counselor. If you don't know a good one, contact a couple of the schools for names.
Ya, and on the house thing? No go.. This is your space. The kids and you. It should be a safe space.. Since my H comes here to fix things etc. I have requested he knocks, calls before coming and stay downstairs. I respectfully said I would not wander around your place without being invited so please realize I need a space of my own too.
I think the fact he is at his parents and has no space to call his own is a bit of a wake up call for him and now he is seeing what you have and wants it.
I think the call of cake eating is pretty darn close.