J, as a woman who's been in your wife's shoes I applaud you for even considering working on the marriage. There were multiple things... selfish things... that took my husband and I down paths away from God, but we are still together today primarily because God is a healing God.
Due to my husband's lack of attention toward my daughter and myself and a history of abuse I was given an excuse to dwell on the desire for other men and another life. That I lived a life of sin is no secret, but that we have a stronger and more open and trusting marriage after so much hurt is nothing short of a miracle.
I hope that these few little bits of insight will help you as you navigate through so much hurt and uncertainty.
1. Your first responsibility is to your God, not to your family. Obviously God is perfect, but through sanctification your heart and mind are not in bondage to the hate, fear, and anger that your human side feeds on. Before deciding to do anything in your marriage, even at the best of times, you have to ask yourself if you are doing it for personal gain or to show God's love.
2. Your second responsibility is to your wife. I don't know what circumstances led up to her infidelity, but if there's even a shred of possibility that something in your marriage was lacking you have to start a step-by-step process of repair. What got me to agree to drop the divorce from my husband wasn't regret in my actions. It was an understanding that I voluntarily entered into a holy covenant with the father of my child, and I had to stay in it with open eyes as long as he wanted to stay married. He had no longer been abusive, so my only grey area of reason for wanting a divorce was no longer gone.
It wasn't his apologies and promises to ameliorate his negligent behavior that drew me back to him, but his actuation of his first promise to love, HONOR, CHERISH, and obey until the Lord saw fit to separate us. Be realistic. You are going to fail her at some point; it's going to hurt her; you are going to want to wring your hands of the whole thing and either project or become vindictive... but by keeping your eyes on the horizon you and your wife can come to an understanding of each other's hearts and rebuild your marriage step-by-step.
It wasn't my acknowledgement that I did something wrong that made me realize I didn't have to live in the past. I would venture to say that your wife has memories that she doesn't want to let go of from her days stepping outside of the bounds of marriage. Inevitably she will make choices in those tiny moments of life to either cling to her husband and let him be her all-in-all (in a human sense), or let those memories build into a stronghold in her life that she will never be able to break down alone. She's feeling just as hurt and bruised and terrified in the marriage as you are. Just make it clear to her that you aren't going anywhere, and if she makes a mistake again... don't do something that she can use later as an excuse for divorcing you or not loving you.
3. Your third responsibility is to yourself. I know some might be reading this are wondering where responsibility to self comes in when we are discussing your involuntary desire to cringe, but believe me... if you don't stay married for yourself then you won't be all-in. The same goes for your wife. Sadly, no love of God, wife, or family will be the closing deal for most people coming back from the edge of a cliff in their marriage. If you can't convince yourself to love your wife UNCONDITIONALLY, and forgive her then you will continually have a part of you that is screaming for freedom. It's called humanity... the desire for self-gratification. You have to commit yourself to being satisfied with Leah or you will be plagued with thoughts of everyone else being responsible when you become less than completely satisfied in your marriage.
4. Where do the children or the rest of your family and church family fit in? What about your testimony. As long as you have a firm grip on conviction on the first 3 points, you will barely be phased by what goes on with everyone else. Before children was a commitment between you, that woman, and your God. By keeping that triangle from being broken your children will no fall by the wayside. At times they may struggle with fears or anger concerning trouble between mom and dad, but if they see that dad is committed to God and mom they will at the very least see half of it right. No doubt, if you are a parent, you have spent time trying to cultivate in your child and understanding that one is to not act on every whim and emotion in full strength. If you remain consistent and an example of a believer in word and in conduct (no matter how much God's hand has to keep your heart still inside) your kids will make their own decisions with an understanding from their father that they are to be God honoring. THAT is the basis of a successful parent.
BTW, I can talk to my husband about possibly Skyping or emailing with you. You need a support system that will help and not hinder that rebuilding process.
. May the Lord comfort you and heal your broken heart. Go to Him for healing and understanding. 
