Something I would do if I were in your shoes, is ask your WH how he intends to earn back your trust.
He lied to you while you were in counseling. How is he going to prove to you that he's now telling the truth?
He re-kindled the A. How can he prevent that from ever happening again, with OW or with someone else? What extraordinary precautions does he plan on putting in place to ensure he remains faithful?
I re-read what I wrote and I think I need to explain it a bit more.
The reason you ask your WH how
he intends to earn back your trust, and what EPs
he plans on putting in place is that you need to put this work on
him.
See if he takes it seriously.
See if he puts thought and consideration into how he can make you feel safe.
See if he follows through on his ideas.
He has shown that his words and tears are insincere, but his actions will speak volumes to you.
If YOU put the effort into trying to figure out what would make you feel safe, and then YOU enforce the boundaries and precautions by checking up on him all the time, then you enter into a parent/child relationship with you being the police, always checking up on him and him doing nothing but trying to stay out of trouble. You cheat him out of the opportunity to be an equal partner in protecting and nurturing the marriage.
Make him shoulder this load and see what his actions say.
You'll know soon enough if he really wants to be an active participant in a healthy marriage, or if he just wants to cry and profess his sorrow until you leave him alone and quit bugging him.