(crap story...i know...,
That depends on you, and how realistic you intend to be with your expectations.
By way of background, I had been married for 13 years when my wife admitted she had an affair. Our relationship has changed dramatically, but we will be celebrating our 24th anniversary this year.
Monogamy is not the natural human condition, it's one we have imposed upon ourselves. Some people take to it well, others (probably most) don't. I'm very sure that your girlfriend had and has no intention of hurting you, and that she values your relationship. I'm just as sure that, if she has not so far, she will cheat again. It is unfair of you to expect her to be monogamous.
I don't know what your influences and worldview are. Perhaps for you, monogamy is an essential feature of a strong emotional bond and commitment. If so, your relationship with the woman will be very difficult, long-term. On the other hand, if you want to/can separate the two, you can probably be very happy making a life with her, even though the relationship is not monogamous.