Hey buddy sorry to hear about this... first thing is first your marriage is over so no point in getting angry. People fall in and outta love all the time the main concern is making sure this has as little of impact on your daughter. I'm sure you know that you sound like a good caring fella. Always be happy in front of you "wife" when she is around.... next absolutely make sure you can prove she is cheating g on you and that's the reason the marriage ended! You don't want to pay her money for alimony. Maybe even speak to a lawyer before confronting her, that would be best just so you know what to expect with child support,property bank accounts ect.. It would be tough to not say anything but make sure you have proof and everything well thought out before confronting her about this. Even a place to stay. Good luck buddy even tho this will end you will be happy and find someone eles. I wasn't married but I have a daughter and I was with my ex for 6 years before it ended and me and her are happier then ever and my daughter is doing fantastic aswell! Tho I pay alot of child support I'm happy to do it cause she is well taken care of by me and her mother.
Good luck! ( go see a lawyer)