My H started and EA that turned into a PA.....how much of a PA I still don't know and not sure I'm ever going to ask or want to know.
BUT, things in our situation didn't change until I started giving him "consequences". And I didn't close him out completely as we have a child together. But I did close him out other ways.
Things are now much much better. A backbone is sexy. Show her yours.
And seriously, the OM not being allowed in your house....that just makes sense. It's just being respectful to yourself and she should be able to easily easily give you that. And how do you know he even wants to be there? I think you have a 50/50 shot with that. I think there are lots of OP who won't go into the marital home.....because to them (and this is sort of funny) going into the marital home is just too creepy.....really lets them feel how crappy of a person they are.