Caught ex having sex when we're trying to work things out. Should I continue to try to make this work?

Hi, sorry that the intro is a tad long but it's probably better that you get more of a back story instead of wondering about the circumstances.

So I broke up with my girlfriend of 13 months after a big fight. There were other factors that led to this decision (not very religious but I am, she has a daughter living at her old ex's who she could be spending more time with, my family & friends don't think she's good for me, etc...) but the fight is what set me over the edge. I left her heartbroken and in tears.

Gradually we started talking again and I explained to her that I was willing to try to work it out but we have to go slow. I screwed it up by letting us get too close too fast, and she would spend the night 2-3 times a week. I would be very affectionate to her, but never say I love you.

But, after she would leave, the next day would always be a roller-coaster ride of feelings. I would say we need to spend more time apart, etc... Basically being a dumb guy, feeling distant and wanting space when she wasn’t around. I figured that if it was meant to be we would eventually get back together. She just *really* wanted me back, and it was hard to say no. And just an fyi, I am insanely attracted to her physically, so many times I fear I’m thinking with the wrong head. :x

I was not looking into dating or seeing anyone else through this whole ordeal.

A month passes, and we spend a nice weekend together with her daughter, me playing surrogate daddy like usual when she's around. Then Tuesday she confronts me about why I'm still distant. I told her that I feel more like friends than a couple at this point and we need another mini-break, but not before we get drunk and she spends the night again. (Feel like such a f**king flip-flopper)

Friday rolls around she calls me to see if we’re hanging out this weekend which we were. I explained I was going out with a guy friend tonight, she says she was going out with the girls. I say we should meet up and she declines, which is odd for her. My intuition immediately creeps in and I decide to go back to her place at about 2am or so. I catch her there having sex with some other guy. I tell him to leave and basically chastise her for hooking up with someone else and how she forever messed “us” up. I also tell her this is the last time you’ll ever see me.

Roller-coaster emotions come back when she calls the next day. I tell her that I’m still in love with her and she technically has the right to see other people. *BUT* to do it so soon after we slept last (3 days earlier) AND the fact that she was going to see me the next couple of days and I’m sure would pretend like nothing happened, put me on the verge of never really seeing her again. Long story short I agree to continue to try to work things out.

[cont. below]
Updates:
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Am I setting myself up for failure? I know if we got back together right now she wouldn’t cheat on me and would put 100% into our relationship, but the fact that she’s willing to have casual sex with someone right after we talk
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...(while I am still depressed about the whole thing and don’t even hit on other girls) tells me I should turn away from this NOW. Keep in mind I really do love her and could see us together with the help of some counseling.
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...Right now I’m having roller-coaster emotion overload which is affecting my work, and this feels like the most difficult decision I ever have to make. Thanks for any input.
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UPDATE: Thanks all. Talked to friends & family to help me sort my feelings out. Sent her a final Dear Jane letter and we're over. Will begin the healing process now. Thanks again for listening and giving your advice.
Caught ex having sex when we're trying to work things out. Should I continue to try to make this work?
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