I struggle with the same problem, not the cheating part, but the not wanting to give AH the keys to his truck. But, I don't drive him anywhere except to his kids sporting events if he wants to watch, and while it may appear that I have no responsibility for what he does, the reality is I will pay the consequences if he drinks, drives, and either gets a DUI or, God-forbid, gets in accident and kills someone. Why? Because we're married, I'm the primary earner (only earner), and we have assets that are recoverable if someone sues us. If he gets a DUI, our rates go up - and I pay the insurance. Actually, worse case scenario is my insurance gets dropped, because 2 1/2 years ago, my oldest daughter got into an accident with a dumpster and was convicted of DUI (thankfully she went through treatment and is doing very well now).
So, if he wants to go to a bar, he has to walk. Now, my AH is the non-violent type, which makes this a little easier. And, long-term, I'm working on an exit-strategy that protects me from any of the consequences of his behavior. I get one of the principles of Alanon is that we have no responsibility for the alcoholics behavior, but legally, that may not be the case for everyone. Part of taking care ourselves has to include taking care of ourselves legally and financially.