I know it's really hard because I have been there. What I ultimately had to do was come to the realization that my idea of my partner was not, in fact, who she actually was. Actually, she was a serial cheater. Cheaters cheat. Once I figured this out and accepted reality, it was much easier to un-couple. And yes, I fully agree, emotional cheating is cheating.

Only you can decide if what you have is worth this heartache. If it were me, I would lay down the law. You're either in the relationship full-tilt, or you aren't.