Hello burning heart and welcome, I'm sorry you find yourself here.
I would hold off on the letter.
We have very similar situations. My WAW moved back in with her parents as well, changed her facebook name/status, is going out with friends, etc. Block her, stop snooping for your sanity.
Get your own life without her and be happy, make yourself into the person only a fool would leave. You were once a whole person without her before marriage, become that person again.
Don't fight her on the divorce, stop bringing it up, and respect her wishes not to contact her. Take this time to address your isses and work on yourself.
Marathon not a sprint.
H: 29 WAXW: 30
Bomb Drop- 9/9/13 Negotiated Settlement- 5/9/14 D Final- 5/21/14 XW has breakdown in attorney lobby- 5/30/14