OKay here's a quick reply from a cheater. The problem is, hubby and I started out this way, I had an affair, I wanted DESPERATELY to make it work and keep the person I had an affair with. We also went to a lot of lists for poly mono. Lists I have since left because of the attitudes of the 'poly' side.
Forgiveness. Still figuring this out, what it means, how to do it. We are actually in therapy now. It's been more than six years. We are in a better place but our issue is that forgiveness is NOT a clean slate. I dont' get that shit at all! We are all adults, let's be honest. As nice as it would be to have a clean slate at times in our life, you don't get one. You can't change what you've done, even if you feel badly about it so the idea that ANYONE is owed a clean slate is utter BS.
Now, as far as actually forgiving your wife and moving forward, I'm skipping the whole whether you need to keep or dump your gf. Can you ask her to take a break, that you need to back off and work on your marriage? Sure. But for a group of people that feel that you only NEED to do things that mean you stay true to yourself to say that the person cheated on MUST anything is crap. Yes there are maybe one or two people here that cheated, kept the person they cheated with and still worked out the marriage. MINORITY. Sorry, is true. The idea of knowing that this person, not just your spouse, but this other person has also decided you weren't worth telling the truth to, worth the respect of backing off, well that's crap. Again.
Here's just how we started to heal. I hope it helps. I gave up my right to privacy. Obviously I was lying and cheating and couldn't be trusted. Trust had to be built. So if he wanted to, he read every email, every IM, every text. He was privvy to every phone call. IF he wanted. At first yes he really wanted. As time went by and I built up trust, he didn't feel the need to anymore.
When I got involved with someone again he was apprised of every step. We are talking, we said I love you, we had cyber sex. Details, only if he asked, but THAT is how you build trust. By being honest and slowly showing that you are not going to lie again.
Saying she can't date, well right now she probably doesn't want to. It blew up in her face. But sayign she can't means that when she does want to or gets the infatuation with someone she'll probably lie. To you and herself. Been down that road to. If we don't SAY we love each other it's just friends and it's fine! It wasn't, we were lying to ourselves and so then to my hubby. So tell her it's not a no dating, it's a take a break for now, build up trust and so that she DOES tell you when she is interested in someone, when she is talking to them.
Sadly, there is an overwhelming feeling in the poly world that most cheat because they just didn't KNOW they were poly, so it's more easily forgiven. CLEAN SLATE. It's not. People who are cheated on know this. there is no clean slate, there's pain and you have a right to it. You also have a right to grieve. Now decide. Move forward, or cut losses. If you are moving forward you have to ACTIVELY work on trust building. It's hard, but her lies and cheating have basically destroyed the foundation of your house. Time to rebuild, and it's a bitch.
Good luck.