G.♣.
If she came to you to try and work things out, would you assume she was saying that you were right and she was wrong? I wouldn't, and I don't think she would either.
You don't have to approach her with an idea of who's right or wrong. You could just say, "Mom, I love you, and I'm sorry we fought," or "I'm sorry I hurt you." Or not say sorry at all, just I love you. Maybe you two have things you need to work out. Maybe you just need a cooling off period.
You want her to come to your wedding but not her husband? Ouch! I'm not sure there's any way that that won't end badly. He might not be your father, but he is her husband. They're kind of a package deal. I think I would think long and hard about that one. Is there anyway that you can just tolerate him being there? As the bride, there will be so many, many, many people wanting your attention and things going on. Maybe you could have one of your friends or relatives run interference for you.
If you give it some thought, I'd be willing to bet you'll come up with a way to allow him to be there without you even noticing.