Is it permissible to slaughter the sheep that a mother vowed for the recovery of her son—knowing that the recovery rate is 90%—and is it permissible for the son to slaughter it with his own money, and is it permissible for the household and relatives to take from it, and is it permissible to slaughter it on the 27th of Rajab?

It is permissible to slaughter a vowed sheep before complete recovery, because a vow contingent on a condition permits the performance of the vowed act before the condition is met. You may slaughter the vowed animal on behalf of your mother with her permission.

As for feeding relatives from the vowed animal, it is permissible if they are in need, or if they are wealthy and it is customary to do so.

The distribution of a vow of obedience depends on the intention of its owner. If he intended it for the poor, he may not eat from it. If he intended it for his family or companions, he may eat from it.

The belief in a specific virtue for the twenty-seventh of Rajab has no evidence, and it has not been proven that the Isra (Night Journey) occurred on this day. Therefore, slaughter should not be specifically allocated to this day; rather, it should be slaughtered on any other day.