she said that this is going to be a problem going forward as everyone knows so she will always feel guilty.
I would remind her that guilt is a good thing, not a bad thing. It is our conscience's warning alarm that something is very wrong. Adultery is very wrong. If she didn't feel guilt, there would be something wrong with her.
I would let her know that you are willing to work on the marriage if she ends her affair and commits to a program of recovery. But that there is no hope unless she ends all contact with the OM. She will laugh at you at first, but you need to put the offer out there to lead your marriage out of the ditch. You can hand her this check list of your expectations:
From Surviving an Affair, pg 66-67
The extraordinary precautions do more than end marriage-threatening affairs; they help a couple form the kind of relationship they always wanted.
These recommendations may seem rigid, unnecessarily confining, and even paranoid to those who have not been the victim of infidelity. But people like Sue and Jon, who have suffered unimaginable pain as a result of an affair that spun out of control, can easily see their value. For the inconvenience of following my advice, Sue would have spared herself and Jon the very worst experience of their lives.
Checklist for How Affairs Should End
_____The unfaithful spouse should reveal information about the affair to the betrayed spouse.
_____The unfaithful spouse should make a commitment to the betrayed spouse to never see or talk to the lover OP again.
_____The unfaithful spouse should write a letter to the lover OP ending the relationship and send it with the approval of the betrayed spouse.
_____The unfaithful spouse should take extraordinary precautions to guarantee total separation from the lover OP:
_____Block potential communication with the lover OP (change e-mail address and home and cell phone numbers, and close all social networking accounts; have voice messages and mail monitored by the betrayed spouse).
_____Account for time (betrayed spouse and wayward spouse give each other a twenty-four-hour daily schedule with locations and telephone numbers).
_____Account for money (betrayed spouse and wayward spouse give each other a complete account of all money spent).
_____Spend leisure time together.
_____Change jobs and relocate if necessary.
_____Avoid overnight separation.
_____Allow technical accountability.
_____ Expose affair to family members, clergy, and/or friends.