How can you Forgive Someone who Betrayed you?

I need your help. I was deeply betrayed by my sister. I was married previously. While I was engaged my sister had sex with my fiance. I didn't know about it until we were divorcing a year later. I was told by my ex-sister- in- law. I was crushed and devastated. I couldn't believe she could do this to me. We were inseparable as kids and thoughtout our twenties. We had gone through so much together as we were both single mothers. Her daughter was named after me.
I was so hurt I couldn't even speak to her about it for two years. I kept it to myself. When I starting seeing my second wonderful husband he encouraged me to write her a letter. I did and asked her to tell our mother what she had done. I had previously told our mom and she told me I was lying. I wanted her to explain why and how she could do this to me.
When I received her letter I was shocked. First she told me I had humiliated her by having her tell our mother. Her explanation was " she was having a bad time in her life"! She never said sorry and even indicated I was a bad mother. In my letter I  had asked her why she had not told me before we married because I would have never married him and put my son through that. That's when she said I would have even if I knew.
I tried and thought I had moved past it. I just came to realize just exactly what kind of person she was. I thought I had barred it. Its been over 13 years now. My sister has again done something outside of her marriage. When she told my mother and I about it. She spoke about it as if she were telling us what she ate for lunch. This caused all the pain and feelings of betrayal to flood back.
This was a man I had loved at that time. I need to understand why and how. I think because she never accepted responsibility for her actions or simply said sorry I haven't been able to move on.
I sent her two text messages trying to explain to her how I feel. I have received no response. How do I move forward and allow her back into my life if or if she doesn't talk with me about this? How can a sister do this?
Please help me and give me your thoughts on what to do.
Thank you,
Christine