I can't speak to them coming back, but my thoughts there are that they always do love us. Somewhere deep. When they have faced their issues enough and want to come back, they find a way. I think But I'll let others chime in.
As for the letter? I think no, don't send it. Send it to yourself. It has the gratification of having written it and sending it, without really sending it to the person intended. It belongs to you and is your thoughts. It won't matter to her except to piss her off and stress her out. It'll show you care and it'll make her feel guilty for leaving. That causes stress and that is often dealt with anger, which results in guilt.
She knows how you feel. It's not about you, Tad. Wish it was. She wishes it was too, but it's not. Sending the letter would harm more than help IMHO.
AJ
"Our lives begin to end the day we become silent about things that matter" MLK Put the glass down... "Yesterday I was clever so I wanted to change the world Today I am wise, so I am changing myself."
But I'll let others chime in. 