What a difficult, difficult situation. If your dad has high-functioning autism, it will be difficult to convince him she needs help since he has a “rule” that help isn’t needed when the situation changes. As you pointed out, he got you help only when he was told by someone else that you needed it. He didn’t come to that conclusion on his own. For that reason, I think you probably need to find a way to get another adult he respects to tell him what to do about your sister.
I suggest you talk to your therapist about inviting your sister for a visit to your grandparents and having her go to therapy with you as part of some sibling sessions. It’s possible that the therapist will then be able (with your sister’s and your permission) to invite your dad in to participate. She can inform him of her impressions and perhaps can impress upon him that your sister needs care.
Meanwhile, please look into whether there is a private school or residential program for people with autism that can offer your sister the support and practical help she needs. I’m concerned that being home-schooled is increasing her isolation. She won’t learn how to handle other people’s mean behavior by removing herself from it. She won’t find friends in the house. You could contact the school’s special education department to see what they suggest. Contact an educational advocate to see if the school is obligated to fund an alternative approach to her education.
I wish you well.