I deeply admire the courage to talk about the transition you’ve gone through and the issues at home. Your mother’s poor behavior with you is unfortunate, but I believe trying to directly focus on her would miss the opportunity to get your father more involved.
By your father not challenging your mother he is not protecting you. When your mother goes to him to complain about you — does it in a way that is designed to make you feel guilty, and your father just lets this happen indicates that your father needs to be encouraged to take more a protective stand for you.
I’d begin by finding ways to connect with your father. Talk to him about what is happening at school. If your mother isn’t a stable ally in the family do what you can to make that person your father. In building the relationship you may not only t=strengthen the bond between the two of you, but you may also be cultivating support that can be used when your mother takes to calling you names.
By developing a relationship with him you are attempting to bring and effective balance back into your life. This should be of help to not only you but also your sister.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral