I wouldn't send the letter. Let it drop.
But it's your decision and sleeping on it for a day or to is the wise "48 hour rule," i.e., if it's a good idea now, it'll be a good idea 48 hours from now.
And may I ask how many of the wrongs she's visited upon you has she apologized for?
You're human. You were hurt and pi$$ed. And possibly, quite accurate.
imo, fwiw. my $.02, etc.

Gardener

"My soul, be satisfied with flowers,
With fruit, with weeds even; but gather them
In the one garden you may call your own."
Cyrano deBergerac