He has shown you who he is....believe him. He is not respecting your boundaries by continuing to come by when you've asked him not to. My personal opinion, if it was me, I wouldn't really care what the "cause" of his cheating was. People treat us the way we allow them to treat us. You've sent a clear message, you don't allow that kind of treatment. So keep your boundaries. Go No Contact. Block text/phone/email. Don't answer door. Tell him if he is clean and sober and in healthy recovery in one year, then maybe you can talk. But don't sit around for a year waiting. Take care of YOU.