What is the ruling on a husband saying to his wife: "I swear by divorce that you will not enter my mother's house," knowing that the house is registered in the name of the husband's father?

It is not considered whether the house is registered in the father's name if the mother is the one residing in it. If the wife enters the house of the husband's mother, the husband breaks his oath and is bound by divorce according to the majority of scholars, contrary to Sheikh al-Islam who believes that expiation for the oath is due unless the husband intended to bring about divorce. The opinion of the majority is stronger, so the wife should be cautious about entering the house of the husband's mother. Assuming divorce occurs, she can be taken back before her 'iddah expires, unless it was the third divorce.