Relationship advice!?

I think I love this girl, shes very pretty, shes very smart, but theres something that is missing. The was pionate unlike most ... this was real chemistry. She cheated, I got mad and we stopped talking, we fought and said some unforgiving things. She is still friends with my sister and my mom and I really want to talk to her but I feel like our relationship has died? How can this happen in as little as a year? I'm still very disgusted looking at her or hearing her. I don't want her around anymore, it feels like it brings back old deep memories I don't want to relive. How can I get her to leave, or come to a mutual understanding that I don't want her around anymore because of this dilemma. Mind you every time we talk its pure chaos.