A letter will only be seen as -- at best, "pursuit" and -- at worst, "holier-than-thou."
May not be FAIR that that's how a wayward will see it, but it's pretty much universally true.
A betrayed spouse should own up to their side of the street's mess, and their side only. Their wayward spouse's side is theirs, as is their destructive choice to have an affair rather than try to work with the betrayed spouse on the marriage (or at least have the decency to end it before getting involved with someone else).