I don't have a sister, but I know how difficult it is when family shuns us. It hurts like no other hurt in the world. Especially when we KNOW it goes against EVERYTHING that Christ taught on earth and it's coming from people who claim they are Christians. Just know that I understand and sympathize. Your letter was necessary and very genuine. I hope your sister isn't ignoring it, but maybe taking some time to think about your words. Sometimes I give the healthiest response when I mull over it a day or so.
God bless sweetie!