UF_Pike You are too much.
Kevlar, do you have summer events with your fraternity? Are you in summer session? I think this situation might blow over by the time that the fall semester rolls around. I wouldn't worry about it too much if you don't have much contact with her this summer. Maybe the invitation is her attempt to extend an olive branch. I don't know all the details, but if I were bad mouthing someone and were called on it in front of a bunch of guys I would do something to make it up to the person I hurt. Maybe I'm off base.
You can be the gracious one in this situation. She cannot undermine you with your fraternity. She has no control over that situation. You are right to try to have limited contact with her, but always be a gentleman. The closest we came to this type of situation in my sorority was a really bad breakup between one of my sisters and a fraternity brother. Out of our respect for her we never mixed with that fraternity. We didn't have a house so that wasn't an issue.
So I just read your update. I hope that it works out.