I think it really depends (the letter) on your motivation. If your intent is to control how she is acting right now, then yes, your sponsor is right.
We can't actually change anyone (and really why would we want to). If your intent is to just let her know that you realize what you have done wrong and what you are doing to fix that and to apologize, well, I see no problem in sending that letter.
If it contains all the ways she was wrong that led to how you treated her, then it will only add fuel to the fire . It shouldn't be about her.
Do you want her to return now, or at least right now, with this new knowledge you have?