Just my two cents. But I think your husband thinks he has been daydreaming with OW, and never really intends to move in with her. He thinks his life is going to continue as is, nice and safe. He can date her while living with you. Now you've taken a step and found a place without him. I don't think he realizes how seriously you take his playing with OW. She's been sending him apartment links for months, and he's done nothing about them. If he was motivated he could have moved out before this lease ended. He's not very motivated.
I agree with this Sue. I learned to judge my wife by her ACTIONS, and not her WORDS while she was wayward. It was hard to do at first, but it served me much better.