Well, normally the problem in transitioning from cheating to poly comes from overcoming the broken trust of the person who was cheated on. Since you're ok with things, that's that out of the way. However, another barrier can be in the person who cheated overcoming their impulse to be secretive or untruthful about the relationship. Some people seem to strangely prefer secrecy to honesty. I guess it's less scary. If you two want to be open with each other going forward, she's going to have to make sure she's doing the hard work of transitioning to honesty.
I find it kind of concerning that she's not ok with you having an outside relationship (is it that she has a particular problem with this woman, or would she be likely to be wary and closed off to the idea of you being with any other woman)? This could lead to serious resentment over time. I would ask her to examine her feelings about that. Why is it ok for her to have another lover but not you? Could she get accustomed to the idea in time?
In all frankness, her actions and attitudes thus far seem really selfish to me.
It seems like there's every reason to believe you two can be fine, but I'm not sure why you're not more bothered that she would be ok with deceiving you for so long, bringing a secret lover to your bed when you were supposed to be monogamous, etc.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.