I have a different point of view here. Depending on how much your drinking affected their lives there may be more to this than you think. You may want to consider AlaTeen for your older son or therapy for both of them. There could very well be a lot of issues he is dealing with. In particular he may be dealing with repressed anger at feeling he needed to cover for you or handle responsibilities that were yours.
Children of alcoholics often grow up to become alcoholics or marry them. I married one and skated close enough to the edge that I decided that I would never drink again.
You weren't the only one effected by this disease.