Yikes, there's too many replies for me to fully read.
Hear's what I think.
Sit back and look at the relationship as a whole. Is it worth fighting for? It kinda sounds like you're already fed up with it anyway, insisting to her being overly dependent on your attention, manipulative, and a liar. Define the extent of cheating in your own mind. Maybe it sounds stupid but, to me, making out and having sex are two completely different realms of cheating. Of course, I'd still be upset over the former, but atleast it can be worked through (IMHO) as opposed to the latter.
You say this guy is a player and gets drunk. Was this a one time thing where he got her drunk and made out with her, or has this been happening for awhile? I'd get the full set of facts from Jane and Mary both.
If/when you do decide to end it, do so tactfully (sp?). Don't stalk/spy on her and try to catch her in the act. That just seems contrived to me. Don't bother trying to keep the peace between her, Jane and Mary. Something tells me that'll all fall apart on it's own. Confront your gf and tell her you've become aware that she's been seeing someone behind your back. When she asks who told you just tell her that's not important, end of story. End it gracefully, but mercilessly if that's your position. You'll still be in good light from her family's point of view (provided they're told the truth), as you've done nothing wrong. I doubt, however, that you'll be spending much time with them ever again as it would be awkward.
My last gf cheated on me as well. I had done nothing wrong and everyone knew it. She wasn't even "unhappy". What happened in the end was all of our mutual friends sided with me and essentially shunned her for her actions, how she dealt with the whole situation, and certain events that followed close after. (Let me just say she dealt with it the worst way she possibly could). Her family, especially her mother, absolutely could not believe what she was doing or why, but sympathised with me. But even after you "save face" with all those people, it doesn't help the crushing feeling of being cheated on. Only time will heal that wound.