That is a very rough situation, I would feel betrayed, devastated, and angry. I might be able to forgive alot of things, however, to tolerate a child from another woman is a little to much to swallow. First of all, you cannot be with your wife and the baby's mother. If the wife had problems getting pregnant and he loved her that much he would of find a way to work it out and find a solution. There are many options other than having an affair and breaking the trust bond.
Obviously, his behavior did not match what he was saying "I love you" to his wife. He chose another woman over his wife, he wants to stay with her, that says alot. I would leave, there is no fixing that problem. If he did it once, what makes you so sure he would not do it again? He had no business. However, everyone is different and have different views about certain things. Wifey got to make a decision and have to live with it and be OK. No one can really answer that question for her, but again if it were me, I would have to get a divorce, I just couldn't deal with that.