What to do with this girl?

I had a girlfriend that I really cared about. She had dated a kid about a year ago. Call him john. They had dated for a couple years before we started dating. This girl was rather promiscuous but i didn't care, i decided to go for it anyway. We dated for six months, then broke up. Got together a couple months later, and just now broke up again. She said she wanted to be friends and all that. Then i found out that she went and had with john three days after we ended. Three days! She says she loves him and that was her justification. Total crap, and i told her that. She says she still wants to be friends and am very hesitant to tell her i don't want to be friends anymore. I sound like a moron but yeah. She did some stuff like this in the past too. I know i should just say forget it all and ditch her completely, but i just can't bring myself to do it. Any suggestions?