I'd acknowledge the hurt she's caused so she knows I'm being honest. I'd expect her to be afraid of superficial forgiveness and afraid I would punish her in little ways forever. I'd be honest with her and then lay out my plan for healing our relationship and putting the family back together.
I'd explain to her exactly what she needs to do to make amends and what I was prepared to do and how I was prepaerd to work with her.
In my view a letter gives her something to read and re-read and gives her a map to follow if she really wants to come home.
If you thought it was something you might want to do, I'm sure some of us would be willing to give you some ideas as you developed it.
