What is the ruling on my daughter marrying the young man who divorced her three times in an urfi marriage, after her divorce from her first husband?

Your daughter's relationship with this young man is a great evil, an act of disobedience to Allah, and a dereliction of her husband's rights. She must repent. If her husband swore an oath of divorce to prevent her from speaking to the young man again, and she did speak to him, then the divorce takes effect according to the majority of scholars. The young man's marriage to her is invalid, whether the divorce occurred or not, because she is either still under her husband's marital bond or in her waiting period ('iddah), and both scenarios invalidate the marriage by consensus. The three pronouncements of divorce are of no consequence due to the invalidity of the marriage. It is permissible for him to marry her after her 'iddah from the first and second (husbands) has expired, but we do not advise this if he has not repented, due to his unsatisfactory religious commitment and character. Some scholars hold the view that whoever marries a woman during her 'iddah, she becomes permanently forbidden to him.