He gets a choice; drop OW completely and commit to working things out with you (which includes transparency) or he can take a hike and go live with her NOW. Why the heck are you letting him stay if he has every intention of moving out to be with her? What is being nice to him getting you?
He should come home to find his stuff on the front lawn (boxes and bags optional).
TrentC is wise, and giving you great advise. I found out the hard way that being nice DOES NOT WORK.
Remember that everything is COUNTER-INTUITIVE. I would like to suggest following TrentC's advise and force him to make his choice NOW.
"What is best for my kids is best for me" Amor Fati Link to quotes: https://www.divorcebusting.com/forums/ubbthreads.php?ubb=showflat&Number=2879712