What is the religious ruling on dealing with a father who abuses his wife and children with insults, curses, and profanity, and describes one of his children as an "illegitimate son"?

A father who abuses his children with insults, curses, and slander is an oppressor, but this does not negate his right to dutifulness and companionship with kindness. The children should advise him and caution him with politeness and gentleness, strive to reform him, seek help from righteous people, encourage him to associate with the righteous and attend gatherings of knowledge, and supplicate for his guidance.

If the children are harmed by living with him, it is permissible to separate into an independent dwelling while continuing to show him dutifulness. If the sister is unmarried, seeking a righteous husband for her is a kindness to her. It is permissible to take measures that prevent his harm from reaching you, and this is not considered undutifulness, as "there is no harm nor reciprocal harm."