You've gotten some good advise already. I'm not going to berate you about your sitch. Others have done enough of that. I will say that even though she says it right now, she's probably not really done. She's mad as hell, betrayed and on top of that dealing with the rush of hormones.
Get into counseling. Tell her about it and let her know she's welcome if she wants. Write the letter about your intentions as others have suggested and really, realy be an open book. Give her all your passwords to cell phones, emails, facebook, etc. If she wants, send her little texts throughout the day so she knows where you are and how long you'll be there.
Be available for whatever she needs whenever she needs it without so much as a "I'll have to check". Drop everything and go whenever she says jump. Make the most of the family time you're getting.
Just the fact that she will still let you in the house at all says she's not as done as she professes. Be patient. Time is on your side.
