If he is going to cheat, nothing you say or "require" will stop him - you know that right?
If he wants this girl, you aren't stopping that either.
I dunno. Cheating is a dealbreaker in my world. Some people get past that but I never have been able to do that. Regardless of his sobriety (which you feel is threatened?) I would call it quits over the cheating.
But that's me.