Am I obligated to take my sister to live with me after my mother's death, knowing that my father had previously molested my two married sisters, and what are the consequences of leaving her with my father, who refuses to leave the house?

There is no sin upon you for leaving your father in his house with his daughter. He is responsible for himself and his daughter, legally, as long as he is of sound mind and capable of disposing of his affairs. Your mother's informing you is not sufficient evidence to accuse the father. Your mother's وصية (bequest/instruction) is not binding upon you unless there appears to be suspicion regarding your father and the daughter fears for herself, in which case it is not permissible to leave her with him. Be keen to show filial piety to your father by helping him to be mindful of Allah, and to maintain ties with your sister by fortifying her with taqwa (mindfulness of Allah) and striving to find a righteous husband for her.