Yikes! I am so sorry for your pain right now...others here have very good advice. I can only say what worked for me and as far as I know, I was not cheated on in any way. Just treated like crap and resented.
I did the ultimatum route. It didn't work until I walked out of the marriage. Only then did he begin to take AA seriously. And he is no more religious than I am. He too was concerned about the whole "religious" aspect of it all. But so far, he seems to have embraced the "Higher Power of his understanding", even if he doesn't completely understand it all yet.
He still holds resentments toward me. They still come out sideways. But he is making progress, one day at a time...
I do NOT get involved in his recovery short of asking him how his meetings went on occasion...and usually because it shows I am interested in his life, even though I really don't care. I work my own program. What he does and thinks is none of my business.
Someday, we may be able to work toward having a healthy relationship again...but that someday is far off still...I need to see sustained change, and right now my own change is far more important to me than his.
Stay strong!
~T