What is the ruling on an oath if a man swore to his wife that she would go to her father's house if she did not pray, and then her legal excuse (menstruation) came the following day?

If it is impossible to fulfill an oath due to a legitimate religious impediment, then there is no breach of the oath. So, if menstruation begins before the time of Fajr prayer, nothing is required of you, because what is religiously impossible is like what is physically impossible. However, if menstruation begins after the time of Fajr prayer has entered, and you were able to perform the prayer but did not, then you have breached your oath. It is stated in "Asna al-Matalib": "If he said, 'If you do not pray the Dhuhr prayer, you are divorced,' and she menstruated at Dhuhr time: if the time sufficient for prayer passed, she is divorced; otherwise, not." The ruling depends on your intention behind the oath and the wording. If you intended divorce, then one divorce occurs. If you did not intend divorce, but rather intended to encourage the performance of prayer and to warn, then you must pay an expiation for breaking an oath.