Let me be honest: You can't make your wife understand that it's God's will for you to divorce her - because it isn't. Nor should you deceive yourself into thinking it was God's will for you to engage in an affair - because it wasn't.
God never tells us to do something that He has explicitly forbidden in His Word - never. This includes breaking the marriage vow - the vow you and your wife took before God to be faithful to each other as long as you both live. One of the Ten Commandments states, "You shall not commit adultery" (Exodus 20:14). Jesus said concerning marriage, "Therefore what God has joined together, let man not separate" (Mark 10:9). Society's standards may change over the years - but God's standards do not.
My prayer is that you will face the seriousness of what you have done and repent of it - both before God and before your family. You don't indicate in your letter what went wrong with your marriage - but with God's help there can be restoration, and there can be new life and joy.
The key is to make Christ the center of your marriage - and your life. So far, you have ignored Him and given little thought to the place He should have in your life. Don't go down that road any farther, for it leads only to turmoil and death. Instead open your heart to Christ, and begin again with His help.