Difficult situation.
I think its very normal for children to create an idyllic parent out of a parent who is not. Your very young child is dealing with issues that adult children have difficulty with - he is aware of his fathers drinking problems, and is in discussion with him over his drinking (a lot for a 12 year old to figure out). Of course all addicts lie, and I'm sure Dad is lying to your child regarding his issues.
I think one of the hardest things as a parent is to do what's best for a child when "best" comes with pain. This scenario works well as long as Dad doesn't DO something while your son is in his custody. If nothing bad ever happened then what's the big deal? IF is the key word here. Your Ex's stated record in the past year is a person that has no business having a child in their home. While you have no evidence that anything has ever been amiss, you really don't know what goes on when your son is there. Perhaps your Ex is not drinking while your son is awake then hitting it later....perhaps he is, and your son just doesn't know. Its very possible that your Ex is driving your child while under the influence as well.
If it were me, I would have to move toward relinquishing custody temporarily, no overnights at the very least and NO driving the child anywhere.
As far as what to tell your child will leave that to others that have been there and done that.
Sorry for what you are going through.