I think the decision that he find someplace else to live is a smart one.
You need time. Him being under the same roof and pretending that all is well is not what you need right now; it's what he wants. This is evidenced by his constant use of we and our when he's talking about your new house, your moving, your spare room, etc. Don't get lulled in to having him back if you're not ready.
And you may never be ready. You might, but you might not. You will
likely eventually forgive him, but that doesn't mean you will want him back. He knows this and he's probably terrified by the idea, but that's not your fault or problem. He has done this, and he has to live with the consequences ... he's changed your lives, not you, and he also needs to stop telling the children that it's up to you. He did this.
Take all the time you need to decide what you want to do. Don't let him rush you. You have too many other things going on right now.
Personally, I wouldn't allow him at the birth. Giving birth was when I felt at my most vulnerable. I wouldn't want someone I didn't trust in the room with me, tbh.