It's entirely possible. But then the question of trust comes into play. How could you believe someone that obviously and blatantly lied to you? If she stayed too long "at the store," could you believe it? I mean, 100% believe it? If there is even a little bit of a doubt, then there is your answer. There is an inner strength/respect that one must have, regardless of the outcome.
I can't remember who said it on here, but the gist of it is that some stay out of fear or whatever. It took me a while before I was able to cross the line and see things as they really are. When someone goes as far as to dream/see/sleep with/get involved with another person, then the marriage is long dead.
I'm not saying that you should give up by any means, but reality needs to be seen, too. If you can accept what she has done and fully trust, then go for it. For many, its a deal breaker - and was for me. Do I still love my ex? Yes. Do I trust her? No.
There are moments in this life when you are so confident in the rightness of your actions, that not even for a second do you consider the option that you might be wrong.