What should the questioner do with her father who abandoned her, her sister, and their mother, does not provide for them, does not ask about them, and whose mother refuses to visit him?

You must honor your father and not sever ties with him, no matter how much he wrongs you. You are not obligated to obey your mother in severing ties with him, for obedience is only in what is right. You should honor your father without your mother's knowledge to avoid her anger, while being gentle and kind with her.