No offense, but these two really sound like they aren't dealing with it well at all. I might change my answer and invite neither. I stand by my thought that if you all are adults, you can deal with people you don't like. I do it several time a year (and what I said in my previous post is the short of the story... there was a LOT she did and hurt us both badly with lies and getting everyone to believe her lies for over a year). Now, if we both can deal with her, and even talk to her after everything she did (police were threatened to be involved and eventually she saw a shrink to help her work with her issues), I would think that they could deal with dumb rumors.
IMO, though 30 is not an intimate party and there are plenty there to keep them apart if they like. If you think they really can't be adults and handle it, invite neither. If anyone asks, just say they couldn't come and leave it at that.