Dan, like the others said, don't give her the letter. Writing letters can be therapeutic but it's for you, not her. Write it and burn it.
You've already apologized numerous times to her over this, STOP APOLOGIZING. Volume is not better than quality when it comes to apologies. Apologize from the heart, then let it go.
A lot of LBS's have gone to divorce court only to get slapped in the face with their very own letter of contrition. What seemed like a good way to apologize is now being used against them as proof that everything is their fault and that they should pay dearly in D court. And guess what, the judges do accept those letters as evidence of marital misconduct, and some LBS's have lost child custody and gained a significant alimony and child support burden as a result.
If your W brings the past up again in person then it's OK to humbly apologize again (VERBALLY), but don't initiate any more apologies.
