I wouldnt have him come home unless he is ready to come home...IMO he needs to initiate that..especially if he has flip flopped before. Him coming and going is NOT good for you. If he is going to come home..I think he needs to be fully committed to working on your M- not because you told him to come home. He is a big boy. He needs to start making some big boy decisions.
IMO- I wouldn't invite him over either..let him want to come over..let him start making some decisions. Guys are so much more accepting of things when it is THEIR idea. My H was always more receptive to things when it was HIS idea. Just my opinion for what it is worth.