Is it permissible for the one offering the sacrifice (Al-Mudahhi) to include his family (his father, his mother, and his wife) in the ritual of the sacrifice with a single sheep, and is it incumbent upon them to perform a ritual if the son enters into the ritual?

A single sacrifice (Uḍḥiyah) suffices for the sacrificer and his household—those he provides for—whether they are few or many. It is permissible for the sacrificer to include in his sacrifice those who are under his provision and in his home, such as his parents, wife, children, and anyone he takes in, like a brother or similar.

They are not required to refrain from cutting their hair or nails; this obligation applies only to the sacrificer.