I personally think you may have a chance of recovery if you really show huge changes on your and take a solid, unwavering, firm stance that you are sorry, understand her hurt and willing to show with actions that you wish to repair the marriage and try to help her with her pain.
Time, space, patience, consistency, determination, dedication. These are some of the things I would focus on.
Personally, I know that some people would find this odd. But in your situation I would take a lie detector test and try to answer any concerns of questions she had. About the sexual contact, about your true intentions now, etc. I wouldn't tell your wife, just do it and give it to her.... my thoughts.
I also think you should be readily available for any family social activities and events. I see that as a way "in" back to her heart. IMO.
I had read elsewhere that many betrayed spouses feel that the cheating spouse must do a penance of sorts for a period of time and the cheating spouse during that time must prove themselves as worthy a second chance.
Just because she states she is done, that does not mean she is really done. She had to protect herself and heal. I think you actions and behaviors can definitely over time sway her though.
Other thoughts.... I would offer to move as a family to another location, I would speak to her family and explain that you are guilty of cheating and are now repentant and willing to do what ever actions are necessary to win her back.
Also, I think it would be wise to read as many sitchs here as possible and on marraigebuilders and read books such as "his needs, her needs", "after the affair", etc.
Again, if this were me, I would go to weekly IC for a very long time (I did this with the MC after hubby quit to prove I wanted to work on myself and work towards keeping the marriage), a pro-marriage MC just for me to learn and understand the dynamics of marriage, church (if you are religious) and voluntarily try in some way to show how I occupy my time (see I am not cheating....)
My thoughts again, I would write a well scripted letter stating you angst, understanding, repentantness, how sorry you are etc. I would state in the letter exacting why you feel this behavior was acceptable in the marraige, why you continued on with it (WITHOUT PUTTING ANY BLAME ON THE OW, this is all on you) how you have learned about boundaries and how to handle stressful periods in the marriage, what actions you are taking to better yourself. I would state that you are at her beck and call, when ever, where ever, you are dedicated solely to her and even in the event of her Ding you you still will remain loyal and dedicated to her, etc. That you are willing to honestly and openly answer any questions she has about the marriage, the affair, what you were thinking etc. For her piece of mind.
I also think that many people will D but still watch your actions to see your sincerity and absolute love for the person. A D does not mean it's over. Remember this.
Listen, my sitch was different, but I will state this. I stood my ground for over a year that I was NOT going to give up on us. My hubby could be done with the marriage but I am still standing. And let me tell you- if you were to believe him- he was done, really, really done. I ignored this. I owned up to all the wrong behaviors and actions that I did and I proved that I will not repeat them. Despite my hubby's insistence that we were done, despite his anger and venom- I heald my ground, I NEVER wavered (ok, I really had a lots of thoughts that maybe I should give up, I NEVER LET HIM KNOW THAT THOUGH)
You think she is done and over you. I think she is DIng you to gain back some "power" and dignity but my goodness, I guarantee she is watching your every move. I think you can really prove yourself and maybe win her back. Fight hard for her. I think it will take a very long time though- at least a year minimum. I wouldn't even be surprised if she D's you and starts dating someone else and then still comes back to you, if you handle this correctly. I think she has to follow her path now and through your decisions and actions you can eventually lead her back to you. It's not going to happen today, or tomorrow, or next month, but maybe next year or two.
So the focus should be on the long term- focus on improving you, be responsible and accountable, showing her your love, showing her that you are an amazing father b/c every woman loves her children to be loved and definitely spending as much family time as possible. Family time, offering to watch the children when ever she wants you to so she can have her time for herself to have fun and socialize, to be happy again, a well timed letter here and there (rather than a face to face conversation initially) and your actions are definitely the key to getting back into her heart I think, IMO.
M38, H37 S3, S7 Together 15 yrs Married 8 yrs Bomb July 2008 Inhouse separation "I hate you" "We are over" (too many times to count) Reconciled Sept 2009 (still worth it)