They are cutting off their father for publicly humiliating their mother, for lying about his vows, and exposing her to possible STDs. Cheating is humiliating and leaves the victimized spouse doubting his or her judgement, and sometimes unable to believe people or trust them again. His actions also humiliate them, by pointing to how little respect he had for his wife and his vows. If their mother is worthy of so little respect, why should they, half of her, think that he would treat them better?

Had he respected his wife and kids, he would have divorced the wife and worked with her to make it a clean break, and only started dating the woman after he was free.

He has a lot of work to do. He needs to do it.