Read what my "loyal" girlfriend did. Should I take her back or leave? 10 points!?

I created a fake profile on a dating website, and I approached my girlfriend on this same site. She initially created the profile to meet women for friendships...yet recently she changed her profile to meet men and she also changed her status to single. I messaged her with a fake profile of this handsome black guy with dreads. She opened up so easily to this fake guy and discredited her relationship with me. All the while, she was acting normal towards me while she was talking to this dude (who was in fact, me ;o) Now, I live with her, and I am between jobs. She put me out this fake profile, saying that I have a little job and I don't help her pay for nothing. When I had got home from a trip, we had sex but it ended short due to me being tired. She was obviously disappointed with my performance. I apologized to her, but she dismissed it...yet she ran to the dating site and told this fake guy I create all of the details of our recent sexual encounter! I was so distraught, yet I continued to go through with this gut-wrenching facade. Evening came, and she was pretending to be doing homework and be on FB, but all the while, she was on the dating site flirting with the fake guy (me). She constantly kept asking for his phone number and invited him to work out with her at the gym. I asked her, what if your bf finds out. She responded, "I don't care. He doesn't pay for anything or do anything. If he has a problem, he can kick rocks." Offline, she told me lies saying that she was going to be getting with a girlfriend for the gym and for skating or bowling throughout the week. Online, she was planning on meeting this dude for ice cream and the gym throughout the week. Blatantly lying to my face. Early the next morning, she starting messaging the fake guy about when they should meet that day. I went ahead and told her that the guy she was actually talking to was a friend of mine (even though it was me and her chatting all along), and that he was going to report everything they had discussed to me. She got scared and immediately confessed to chatting with a guy online behind my back. I knew what she was doing all along, yet I played like i was shocked to learn all of this. As of late, she has been begging my forgiveness and entreating me to start over with her. I do want to forgive her, but I don't really want a relationship where I'm wondering who's she talking to. Plus, she just downed me so badly to a complete stranger. She has the audacity to tell me that she loves me all the time...how can I trust her after this? Should I trust her?