First, you know you parents better than we do by a good margin. If anyone knows the right thing to do, it's you. But, you asked for help, so here's my suggestion.
Okay, so the previous posters have offered a whole bunch of ways to say, basically, "Hey, parents, I want you to show up for my wedding, but only if you can behave yourselves. Can you handle that?"
Pick your favorite phrasing, and at some point ask your parents
when they're both in the same room. This way, you not only get an answer, you get a trial run of sorts. You can ask them both separately before if you think it'll make this go smoother.
You should know ahead of time what you'll do if this doesn't work out -- will you tell them both they can't come, choose one randomly, or just pick your favorite? I'd only suggest the last one if you don't mind not talking to the other parent for who knows how long -- okay, I'm only suggesting the last one facetiously, but hey, don't let that stop you if it's what you want to do.
Okay, so now let's be optimistic and assume your parents both agree to act like the adults they presumably are. You'll probably want to appoint a trusted friend or family member to handle any situations that may arise at the wedding, just in case. That way, if things take a turn for the worst, you won't have to get dragged into the mess. Face it, it'll be a lot easier for someone else to handle problems quietly, given that you're kinda supposed to be the center of attention and someone else might be able to deal less contentiously with your parents.
Wow, I didn't realize how much fun it is to channel my inner advice columnist. In fact, I didn't even know I had one. I'm a little disturbed by that...
