The same thing happened in my marriage, but I'm the spouse who was kept in the dark. My husband continued to act out because he figured, "I'm going to hell anyway. I can never tell my wife because she'd leave me for sure. My kids deserve to have a father." As a result he was "with" several other women over the course of four years. I had NO CLUE, so it is possible that your wife may never find out. I ended up finding out completely by accident, one of "the other's" info had not been deleted from his phone. IT ROCKED MY WORLD. I did end up leaving him temporarily. (4 month separation)
He quickly decided having his family back was more important than continuing in his addiction. It sounds to me like you are in this boat too~ you love your family and wife. I'm not going to lie to you and say that things are "hunky- dory" now, but thanks to some great counseling, we are putting our lives back together. I love him now more than ever, because he's done a 180. (I think subconsciously, because he figured he was on the fast-track to hell, he just stopped trying. He didn't want to spend quality time with us, had a short temper, screamed and yelled at us all the time.) He's finally back to the man I married 15 years ago.
I am in an excellent place spiritually thanks to my "new" understanding of the Atonement, and what my Savior suffered for me and all of us. This is what pulled me through, and it can pull your wife through too.
Counseling is a must though for both of you. There are so many people that are keeping secrets from their "Forever Friend". This life is the time to get it out. This is the "test phase".
Just speaking for myself here, but I'd be a lot more devastated when, in the after-life, I go with my Hubby to watch "his life movie" in front of all our family and friends, and all his lies and deceit pop up on the screen.~~ Just something to think about.
Best of luck, I'll be praying for you both.