All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
You should know that you are obliged to show dutifulness towards your father, regardless of his condition. One of the most significant manifestations of your dutifulness towards him is striving to guide him to the straight path, prevent him from treading the path of vanity, and instructing him about his religion. Please refer to Fataawa 85180, 83566 and 87672 on how to invite one’s non-Muslim parents to Islam.
If your father does not actually believe that Islam is the true religion of Allaah, it is impermissible for your (Muslim) mother to remain married to him. It is incumbent on her to seek a marriage annulment. For further information about the religious ruling pertaining to a Muslim woman’s marriage to a non-Muslim or an apostate, please refer to Fataawa 90497 and 90432.
Allaah Knows best.