So you have been acknowledging the A happened, which was 3 years ago, right? But he maintains no sex, although evidence seems to say otherwise?
So in 3 years, what HAS he done?
It seems as though he has been
still lying to you
displaying anger when questioned about the affair
If all of this is correct then he is not remorseful and R cannot happen with someone that doesn't get it.
You have spent 3 years waiting for him to understand your pain and walk with you through R. He doesn't appear ready or willing to do that. Agreeing to MC doesn't work when one isn't open and honest.
When is it time for you to live your life? When do you stop waiting for him to care enough about his family, his wife?
Please don't allow him to dictate the direction of your life.
If I were you (and I am not, so take this FWIW). I would drop the MC, get into IC and start detaching from him.
Let him continue to derail his life.
Take charge of yours and take steps to make it a happy,fulfilling one.
You cannot do R alone.