I can understand that drinking would be a deal-breaker for you, living with an active alcoholic is hell
I see drinking and cheating as separate, both equally lousy coping skills or acting out, if you wish.
My fWH is a "recovered" alcoholic with over 12 years sober when he had his A. Sobriety does not guarantee fidelity.
If it was "just a slip" and he's willing to "get back on the wagon" and he does have a sponsor and is doing (or will do step work), then his slip may not be that much of threat to your R.
I hope you're well. Have you done any reading on co-dependence? This might be a good time to implement the 180 (if he's around) or use it as a guide on how to take care of yourself right now.