Hi Nina,
My deepest heartfelt thoughts for what your family has endured. Sounds like your Dad has made his bed and is lying in it. You have chosen to care for your sister, and that is a beautiful courageous act of love.
Stick to your guns, you will never regret having your sister with you. I personally took care of my terminally ill mother, and never ever does a day go by that I regret that decision.
Good luck, and keeping you close in my heart.