What should a husband do who divorced his wife for reasons he acknowledged, and she now wants to swear an oath that she did not commit those acts, and his father swore to him not to take her back and threatened to disown him if he did?

If the wife is pleasing in religion and character, or if you love her, and your father asks you not to take her back, you are not obligated to obey him in that, because obedience is only in what is right, and there is no harm to the son. Sheikh Al-Islam Ibn Taymiyyah was asked about divorcing a wife at the mother's request, and he replied that it is not permissible, and that honoring the mother is not in divorcing the wife. However, if there is a legitimate reason for the father to request a divorce, such as the wife's bad character, then his request must be answered. But if the request is motivated by jealousy or caprice, the son is not obliged to divorce his wife. The son should deal kindly with his parents and persuade them with gentle words.