Nervous about an open bar at wedding?

We want to have an open bar at the wedding, however, my father and stepmother tend to drink too much at events like this and tend to make a scene. I still cringe when I think about the fight they had during my graduation reception. My father is an alcoholic, and my step mother just can't hold her alcohol. They are both rather mean drunks, and I just don't want to deal with it. I can't bring this up to them, they will get upset. What should I do? I've been reading ideas online about cash bars and drinking tickets, but both seem to be a huge no-no with everyone. I know I should just toughen up and talk to them about it, but I really think it will do more harm than good. Should I just suck it up and cut the alcohol to avoid a scene? Any other ideas?