I wonder if this question were asked in the spiritual room might be more helpful to you. While you may not be as religious as your wife, perhaps there is a spiritual way to reassure her that you are fully committed to her in this life. That you are truly sorry for the mistakes that you've made as a man ~ you're willing to admit these love crimes to a man (or woman) of the cloth, and devote whatever dues necessary to win back your wife's sense of trust and respect.

I would recommend taking that avenue, if you are comfortable with religion. I believe that sharing this with your church leader could be very reassuring to your wife. Whether you go with or without her is up to you both.

Personally, I'm agnostic and don't hold onto any religious beliefs. BUT, I assume that if I were religious, the tip above would be very comforting to me.