Do I give her a second chance to be with me?

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So I have been dating this girl for over a year and we broke up in December and it was my fault, but it was something that could have been fixed. After we broke up we've been trying to fix our relationship and be back together, but at the same time she was seeing someone else. I was fully aware of that, but the other guy didn't. I thought he was just a crush, but they we're going to get serious after talking for 4 months and he didn't know about me. She's been having sex with both of us without each other knowing. We both ended up cutting her off from our lives because of how much she hurt us both. Now it's the day after we told her off, but she completely wants to forget about the other guy and get back with me. I can see it in her eyes, that she's truly sorry and she wants to prove that she can earn my trust back even if it takes years. I feel like I know I shouldn't let her back in my life since she played me, but even after everything, I still love her. I feel dumb cause I want to hate her and I want to be mad but I still care for her, even if she crushed my heart. So I told her that I won't talk to her or expect anything from her, but if she wants me in her life then she has to work like hell to prove her worth. But in reality, am I doing the right thing or should I change my approach?