Anonymous wrote:write her a letter just saying how much you love and miss her and how sorry you are that you've done things to upset her along the way and how you hope in the remaining years you both have on this earth that you can spend some time together. do not mention specific incidents and do not be tempted to place blame at her feet. keep it simple. And stick with it.
I would not do this especially the part about the "remaining years you have on earth."
It is creepy trying to drag the husband into this. I noticed OP got very excited when somebody said the sister is likely mentally ill. That tells me OP is looking to vent and have a bunch of strangers join in the drama. If you truly want a meaningful relationship you would care that you hurt her deeply and you would want to repair it. It sounds like you find her upset trivial and you want a bunch of strangers to validate that.
OP, get help to accept things as they are. You don't agree with your sister about the issues and she doesn't want to be around you. Let it go. Having a bunch of strangers tell you she must be nuts does not help. Dragging her husband in is disturbing. Writing a letter to someone who made it clear she does not want contact is disrespecting boundaries. Move on. Give her peace. Find your own peace.