And what makes you think that this other guy can give her what SHE wants. It doesn't matter if he has a diploma or a good job or whatever else you have said. What matters is how SHE feels. What SHE wants. How you treat her, how he treats her. You are NOT a failure and it's not for you to decide what SHE "deserves."
If you don't want to be with her anymore because you don't trust her, THAT is why you should leave. Not some bullshit about how this other guy is better for her. You can't and don't know that. You don't know this guy AT ALL. What if he's abusive? What if he just wants to steal from her? How would you feel then?
As for the daughter, just because you two split doesn't mean you can't still see the child. It's ultimately up to her, of course, but there's no real reason you couldn't. I still let one of my ex's girfriends see my kids. They were together for 4 years, so she was a big part of their lives. I won't take that away from them just because of petty bullshit.
But, to reiterate. I do NOT think you should break things off. Talk to her about your concerns. If she says she wants YOU, believe her. If you don't trust her or don't love her, that is a reason to move on. Do NOT decide what is best for her, she's a big girl and can do that for herself.