I feel your pain. The number one rule that my group of friends follow is once one of us first mention their interest in a girl, she is off limits to everyone else, and if they break up, it sounds bad, but she is as good as dead to all of us. The pain you feel is the reason why we have that rule.
Oddly enough, I believe that the only way to get beyond the hurt is for you to forgive her. You are forgiving her because her actions shows that she is not perfect. None of us are perfect. If she was perfect, and she did what she did, I would say that she does not deserve forgiveness, but because she is not perfect and makes mistakes like all humans do, I say forgive her. You should also forgive her because you deserve to feel better than the why you feel now: you deserve to move beyond this point. You deserve to enjoy the times that you spend with your friends. You deserve to let go of your ex.. You deserve to find someone better than your ex.. You deserve to be happy.
Now, forgiveness and forgetting are two different things. Like wise, forgiveness and trust are two different things. At this point, you cannot forget what she did, nor can you trust her. You are right in both instance. If you feel that not being around her is the best thing for you to do, you have the right to that decision, and you have good reasons too. But, realize that you are also going to be putting a strain, and constraints on your other friends.
This can only work if you forgive her: I would suggest that you coexist with her around your friends, but put a line up which basically says that I do not trust you enough to let you be apart of my life, but because we have the same friends I have to get use to being around you, but out side of that we do not have a relationship. If you can't do that, someone has to be removed from the group.
Well, I hope that I helped a little. Good luck!