I don't envy you this position. I am guessing you feel horrible about yourself too for being involved in cheating - you feel bad about it, he doesnt, maybe you envy that he doesn't care, maybe mostly you envy that she seems so interested in him. I'm also not clear if she broke up with the partner she cheated on? If not for me him dating her would be a dealbreaker NOW because I'd want to not be associated with that at all.
If she did break up with him.... I'm guessing for ME in this situation I'd say something along the lines of "I don't feel comfortable with you dating somebody who would cheat and not be bothered by it. I feel like a bad person for being a party to cheating, and the truth is that makes feel you're goals are skewed if you know she isn't the most ethical person but want to date her anyway - it makes me wonder if we are compatible in the long run. I want to move forward and only be involved with people who are behaving in an ethical manner. With that said, I can't tell you what to do, but I really don't feel comfortable with you dating her and would like you to take it off the table for X amount of time, and spend that time open to new people. If you decide it's important to explore this, I will work to be OK with it but I might find it's something I just wont get comfortable with and will have to make my decisions based on that.
Not sure if any of that is how you feel at all, but it's what I'd go with for myself....even though I know by now that only works if the other party is honest and trustworthy and won't say things just to placate people. I can't really address the other stuff until I have a better take on that stuff. Ok, now I'm going to go back and read GG's response and see she said it all better and added 20 other useful pieces of advice.
Happiness will never come to those who fail to appreciate what they already have.