You are not the exception to the rule. You will not cure them of cheating, because you're an awesome person. A cheater will always be a cheater. Especially, when they are cheating long into adult years.
Accept that years were wasted on an alcoholic. Accept that you were married to a man who was in denial. Let go of the abuse you took from an alcoholic. Let go of the man who chose drinking over his children and wife. Have faith in what will be.