Honest Opinions: What would you do if your Fiance did this?

Here are the details: Engaged couple together for almost 10 years. Have a child together. Living together for about a year less then time dating. He has a girl saved in his phone under a guys name. He texts this girl all the time and WAY more then he texts his fiance. He talks on the phone to this girl. He has swapped photos with this girl. This girl refers to him as "babe" and "honey". Girl says she loves his eyes. Girl asks him if he is single.. his response is that he is with someone but doesn't know for how much longer. He arranged to meet this girl outside her hotel while his fiance was home with their child and his 3 children from a previous relationship. He told the fiance that he was at work. She believed him. He never told the fiance about this girl. The fiance has never met her and never even knew she existed until today when she found the text messages. He says he just wants to help this girl stay clean even though he only just met her and she is obviously interested in him. Fiance is utterly devastated by all this and feels so betrayed since a few months ago he was flirting and sending pics and talking all the time to an ex girlfriend and he and his fiance talked about it when she confronted him and he said he wouldn't do it again. He thinks there is nothing wrong with what he did. She thinks everything is wrong with what he did. He says he still loves fiance and wants to be with her and wouldn't cheat on her. He says he has never cheated.. I just don't know if he has ever physically cheated but from everything I do know it feels like emotional/verbal cheating at least. I am just beyond devastated. I can't stop crying and I wish I never got out of bed this morning. I asked him if he was only staying with me because he felt obligated to. He told me no and that he loves me. I just don't know what I did to deserve this. I try so hard to make him happy. He says he only said he didn't know how much longer we would be together because he was mad at me that day. I said it shouldn't matter how mad at me he was that saying that is still unacceptable. He said when he saw her in person he told her he was with me and wouldn't cheat on me. I just don't know if I believe that is true or not. But even if he did then this girl just doesn't care if she breaks up a family? Because to me it is obvious that she is into him. What would you do? Who is right? Who is wrong?

If he was my fiancé I would definitely break up the engagement atleast then give him some time to make things right since we have a child together that would be better off with both parents. My reason is that there is usually more hidden issues than the ones you discover and it's worse that he finds nothing wrong with the emotional cheating and so would never be willing to change his behavior on that front. Good luck.