PLEASE listen to Ellie and see a lawyer before you move out -- you may be giving up more than you know by moving out.
Now, quit caving into him -- he is toxic right now, just stay away from his bed. And, document the things he is doing. He should not be having the kids lie for him -- this is a no brainer that may be important if custody becomes an issue.
Finally, try to step out of the victim role. YOU betrayed YOURSELF again by sleeping with him when you knew he was confused and not committed to you. It was a risk you took that didn't pay off. That hurts, but it was your choice. It doesn't sound like any more of those risks are worth taking right now. Now is a time to make sure that you and your kids will be OK. He has no interest in doing this. He will try to get away with as little as possible. And, in my experience, he will keep finding ways to reduce this "little" to "less" as time goes on.
I agree with Ellie that he probably moved back in so he could not be accused of abandonment. He is trying to position himself well for court. You should do the same.
Again, DON'T MOVE OUT without talking to a lawyer. If you have no money, contact a women's center, check out the many resources available through google, etc...
Figure out your rights and don't let SO bully you into giving them up.
If he won't move into the other room, you move there. The important thing is to put some distance there, forget about trying to be "the winner" in that battle.
