Is it permissible for a married man and father, who lives with his parents in the same house, to share in their sacrifice, knowing that his mother prefers him to participate in their sacrifice instead of buying a separate one for himself?

The Udhiyah (sacrificial offering) is a confirmed Sunnah according to the majority of scholars, for every able person. It is not permissible to share the cost of an Udhiyah if it is a sheep. However, up to seven people may share one cow or camel. The sacrificer may include others in the reward, such as his children who live with him and on whom he spends. If a father provides for his son, he may include him in the reward. But if the son is financially independent, it is more appropriate for him to make the sacrifice for himself and his family. Obedience to parents does not include abandoning confirmed Sunnahs, such as the Udhiyah, if their prohibition is merely out of compassion.