Your sister may not appreciate it right nowm but someday she’ll understand what an understanding and compassionate sister you are. From my point of view, this is the kind of situation that demands family therapy. You are correct that this behavior is not normal. She is sending up flares that something is terribly, terribly wrong. It seems that she is blaming you for her inner turmoil. In some strange way, that may feel safer to her than confronting whatever is really bothering her.
I would encourage therapy that includes your mother, you, and your sister. If something happened while she was with your dad, your sister needs to be helped to understand that you and her mom are there for her. Your mom needs help taking her role as the mom who is both in charge and in support of her younger daughter. You need new ways to manage all that hostility that is directed at you. Your sister needs support to tell you and your mom what is really going on with her.
To find a family therapist, go to the AAMFT (American Assn for Marriage and Family Therapy) website at: www.aamft.org/iMIS15/AAMFT.
Thank you for writing. Now take the next step and help your family get the help they need.
I wish you well.