What is the ruling on a son and his mother sharing the cost of an Uḍḥiyah (sacrificial animal)?

It is not permissible to share the price of an Udhiyah if it is a sheep. However, it is permissible for seven people or fewer to share the price of a camel or a cow, provided that no share is less than one-seventh, based on the hadith narrated by Jabir: "We sacrificed with the Messenger of Allah, peace and blessings be upon him, in the year of Hudaybiyah, a camel on behalf of seven and a cow on behalf of seven."

Therefore, it is not permissible for a child to share the price of one Udhiyah sheep with their mother.

It is permissible for the one offering the sacrifice (Al-Mudhahhi) to include others in its reward if they live in the same household and the Mudhahhi is financially supporting the other.

If each of them wishes to offer a sacrifice on their own behalf, then each must slaughter an independent sheep, or participate in one-seventh of a camel or a cow.