I'm a little shocked that people are telling you to just "dump his ass". I think that's a bit of an over-reaction. I'm not saying that what he's done (inviting her to the wedding and then refusing to cut her out at your request) isn't a completely foolish and hurtful move on his part, but that also doesn't make him the devil incarnate.

I think what it comes down to is that he's not seeing this from your perspective at all. He most likely views his friendship with her as innocent (as you determined from reading his FB messages as well), and probably sees your demand to cut her out as controlling (it's not, but he probably sees it that way). My question is: does he agree that his actions from three years ago constitute as cheating/are you both in agreement that this is what happened? It very well sounds like he cheated, but I'm asking because if he views his past actions as valid, it would make more sense as to why he disagrees that he should cut her out. He calls her a "friend" as if she wasn't a past indiscretion. You agreed that they could be friends up until she moved closer/was invited to the wedding...then you changed your mind. You are sending him mixed signals by calling her his "friend" on one hand and the "woman you cheated on me with" on the other. She can't be both. You and him need to come to an agreement on what exactly her role was at the time when this all started.

If you BOTH agree that he cheated on you with her (emotionally or whatever) then the situation is simple: you are asking him to cut contact with the woman who he had an affair with and/or lied to you about because her presence only serves to remind you of that awful time, and choosing to keep her in his life is disrespectful to you and the relationship. I agree with other comments that it would be a good idea to turn it around and have him imagine the situation reversed. I think he's just not seeing the situation as you are seeing it.

I really do wish you all the best with this. It sucks to have an issue from years ago rear its ugly head right before you are about to commit fully to him. Hopefully you two can finally move on and come to an agreement that works for both of you. Personally, I hate ultimatums. I think long term relationships, and indeed marriage, work best when both parties can calmly sit down and find a solution together, without threats. If you can't, then there's probably a much bigger problem.