I think the right way to do things now is to tell people that you're inviting everyone, and they can decide if they want to come or not. It's not fair of them to ask you to choose between the people you love (I mean for instance between your parents and your gf). You're being fair by inviting both and letting them not show up if they don't want to.
But if they do show up, it's their decision, and you expect them not to make a fuss over anything. You should be clear about that to them, that if they show up to the wedding, it means they have agreed, for that one day, to have a truce and enjoy the occasion. If they don't feel up to it, then they probably shouldn't come.
About your gf wanting to come out as well... it's understandable, but I'm not sure if it's the best time to do so. I think the only way to make a decision on that would be for you guys to talk about it (I mean all three of you).