From experience, I have to say I think men can be extraordinarily dense over the more delicate points of relationships. Seems to me that because he himself feels fine about staying with you, someone he already knows well, you and the new woman should feel equally OK with it. I can almost hear the breezy, 'Oh, stop worrying, it'll be fine...'.
If I were the OW, I would feel constrained to point out to him that however HE feels, it's early days and a hotel or B&B is the way to go this time.
I can't help wondering whether money is also a factor. Could it be that he's short, or just tight? Heaven knows it's not uncommon.