Was informing the mother about the father's repeated adultery the correct behavior, and what is the optimal course of action towards this father who does not pray and curses religion?

If the father commits adultery, insults religion, and abandons prayer, he is in grave danger. Insulting religion is an act of disbelief (kufr), and abandoning prayer has been considered by some scholars to be an act of disbelief that expels one from the faith. Adultery is one of the gravest sins. The son's action of informing his mother is correct if the intention is to prevent the evil. The son must advise his father and try to reform him by seeking assistance from righteous people and encouraging him to associate with good people, and by frequently supplicating for his guidance. If that does not work, then the wife must separate from her husband if he insults religion. If he returns to adultery, the son should inform someone who can stop him. His right to dutifulness (birr) does not cease; indeed, one of the greatest acts of dutifulness towards him is to enjoin him to good and forbid him from evil, and to help him obey Allah.