What is the ruling of Islamic law regarding a man who swore an oath of divorce upon his wife that she leave the house, and then permitted her to stay?

The relied-upon opinion for us regarding the issue of swearing by divorce is the view of the majority, which states that divorce occurs upon breaking the oath, whether the swearer intended to bring about divorce or intended incitement, prevention, or threat. Retracting the oath is of no benefit. Based on this, your brother’s wife was divorced by one pronouncement due to breaking the oath of divorce. If this pronouncement does not complete the three divorces, he may take her back during her 'iddah. However, according to the opinion of Ibn Taymiyyah, if he did not intend to bring about divorce but rather to threaten, then divorce does not occur, and he must pay an expiation for an oath (kaffarat yamin). If he intended to make the divorce conditional and then retracted, there is neither divorce nor expiation. One should be wary of swearing by divorce, as it is among the oaths of the dissolute.