Thing is that you gave up control- Basically, she has the control of the situation and now can manipulate it to how she seems fit (i.e. telling her friends that you're talking again, restart the relationship etc.) you didn't establish any barriers, did not set an standards upfront or communicate to her that this will be a sexual situation. You left the door open for a lot of possibilities even though you said it's just sex. The real problem is that during momentary weakness, you let her back even though she violated by cheating. Obviously you still have feelings for her and she knows that. Your feelings may not be as strong as they once were, but they are there nonetheless. Because you still want to chill with her in a nonsexual way too, and then it seems like it will be a routine thing if yall continue hanging out.
But the trust factor is gone- so you have to decide whether to continue down this path and decide if you can take being on the receiving end of her taking advantage of you. Right now, she's getting the benefits while you're confused. I know it feels good because you're with someone that you were in a relationship with and it's emotional. Thats right now though.. how will you feel later on when the emotional feelings fall off and that resentment starts coming in to play. But you gotta decide if you are willing to put the indiscretions in the past, forgive and get over it. Or logically, can you put up with someone who violated your trust. Thinking ahead, what's to stop her from cheating again, then you're left in the same position, Because its kind of like you're giving her a pass from the cheating before; like she already got one over on you. is it better to repair and work on the relationship or should you cut all ties and move on without all this stress. All those lingering feelings will be harder to break from the longer that you stay in the situation. Need to decide if its worth all that.