I know you really need to write this for yourself but I hope you don't send it. I've heard a LOT of words from my husband in the last year and I don't believe any of them. I believe how he behaves towards me. Period.
I know you feel like you don't have the opportunity to have her see you behave but you actually have, and you've already been rewarded for it too, when she sent you that short note. That was appropriate and good.
The fact that she didn't prolong the correspondence means she isn't ready to hear more from you at this point. Your respect of that shows that you really are doing the work. It may feel like inaction, but it's action requiring tremendous discipline.
I recall you ran into her at a party not that long ago? So she's still in your orbit, even if it's just loosely. Those opportunities will not be frequent, but they can still be meaningful, and for sure way more meaningful than a letter, even a carefully written letter.
Has patience gotten any easier for you in the last couple of weeks?
Me42, H40 D12, S8, S7 A revealed: 7/13 Sep 4/14; Agreed to D 1/15