Yet again i find you in exactly my past sich OurCrisis! When my h moved out in November it was with just that professed aim - to see neither of us and to find out how he felt. LOL. In reality he kept in close contact with me (he had the excuse of the kids) and i facilitated this cos i was too terrified to cut him off. Meanwhile he also kept in touch with her whilst lying to me about it! I may be a cynic but i am pretty sure that a request like this is him manoevering for personal space to see more of her while he decides if she will fit the bill for the full time post. The good news for you is that like most males he has no idea how losing his home will affect him. The bad news is that if he continues home contact and visits you for cake eating sessions this truth will not dawn on him at all until it's possibly too late. Having been there, the only thing that affected my h was cutting him off. Reality dawned pretty quickly when he didn't get me for safe base and her for fun. Don't let him come into your home to see the kids - give him a taste of reality post divorce style. He gets to take them to McDonalds etc if he wants to spend time with them. Meanwhile YOU go out looking good - and no, there is no need to tell him where or with who. A situation for him to ponder.
My take on this is he loves you - but he's not feeling it at the moment. Too confused and guilty. His affair was interrupted before it ran its natural course and he's looking to resume it to make this mythical "decision". He has learned from past experience that you will hang in and hold on for your marriage so feels safe to dilly while he decides - he may be under pressure from OW also who believe me will see this as a golden opportunity. Keep showing your natural dignity, don't pressure him but explain your boundaries to him and stick to them. Basically NO contact with you until he finishes any kind of relationship with her. Where he lives is immaterial but he needs to finish this EA. Good luck.
Me 42 H 45 3 kids, 22,12, 7. OW 25 Married 24 years.