I may have a more worldly view of marriage than most people here, and I do believe that it is a contract between two people. The people determine the terms.
If two people agree within the relationship that it is OK to play around, that is their business. That agreement appears to have most definitely NOT been made in this case.
I believe forgiveness is a part of any human relationship, so if this were a an activity involving a couple nights or a weekend here and there, that's forgiveable to a limited quantity.
However, playing around does not mean you actually start building a relationship outside of the marriage. This falls beyond even an open relationship, much less the exclusive commitment you made.
That said, I will not say whether you can or should forgive her. I am in no position to make that decision. My only advice is to leave your daughter out of the decision. The worst thing you can do is to stay with her for the sake of children. Do you think you can have a marital relationship with her again? Do think you can build trust with her again? Do you think you can recapture a special relationship with her again?
Consider those questions carefully. Although I consider marriage a lifetime commitment, my advice it to reevaluate whether you want to be married to her, to make a new promise to her.
The children have no place in this decision. The decision regarding the children comes AFTER you decide on the marriage.
