Should I take back my cheating girlfriend?

I started dating a girl in January 2009, I had already joined the air force national guard when we started dating and we spent long hours talking about how hard it was going to be when I had to leave but we agreed to stay together and make it work. So I left for basic training and tech school (8 months total). And in late May or maybe June we got into a really big fight. She said that we were broken up. I kept asking her to stay with me and she said that it wasn't me she just didn't want to be with anyone, because it was too hard having me be away. Well one day she called me very upset because one of her friends had driven off with her car. They spent a long time looking for him. The next morning she found out that he had been drinking and was driving recklessly in her car, got pulled over, and when the police officer approached the car he somehow got stuck in the car door and her friend sped off dragging the officer. The officer ended up shooting and killing her friend and the car was totaled. I had noticed prior to this that this friend kept leaving suggestive comments on my girlfriends facebook. She denied anything was going on. Well soon after he died we got back together again. When I came home she was there for me with a big beautiful sign and t-shirt that she made for me that said welcome home and that she loved me. So I had been home for a few weeks and she had to go to the ER for a UTI. When she goes in she leaves her phone with me and I started to go through it and found a message that explained to one of her friends that a guy she had been dating got killed in her car. I confronted her about it and we got into a huge fight because she cant stand it when people go through her stuff. She ended up telling me that it was the best way she knew how to explain their relationship because when they saw each other they would always hold hands and hug, but nothing serious. Well I didn't really believe this and I ended up contacting someone who knew both of them. This person told me that she knew my girlfriend and the person who died definitely had engaged ually. So I confronted my girlfriend about it and she continued denying it. She got pissed off that I went behind her back and talked to someone and broke up with me. That night we talked on the phone and I just kept pressing. I said "Hopefully you at least learned that you can't cheat on people", and she replied "I wasn't even with you when I was doing those things". That was last night. We are back together now, but I don't know what I should do. She tells me that she is genuinely sorry for her actions and she isn't going to lie to me anymore. But she is the kind of person that likes to just sweep her problems under the rug and not talk about them. I want her to take more responsibility for her actions and tell me things like; did you love him or were you just lonely? Can I ever forgive the girl I love for sleeping with another man while I was gone, then lying about it to me for months? I love her more than anything, I feel like I can't live without her. I don't know what to do can anyone help?