Should Your Family Avoid Removing Hair or Cutting Nails If You Are Offering Udhiyah?
Question

If the man is the one who is going to offer the sacrifice, is it permissible for his wife and children to cut their hair or nails once the first ten days of the Dhul Hijjah have begun?
Praise be to Allah.It is permissible for the family of the one who is offering a sacrifice to cut their hair or nails during the first ten days of Dhul Hijjah. We have already said in the answer to Question no. 36567  that it is haram for the one who is going to offer the sacrifice to remove anything from his hair, nails or skin. But this ruling applies only to the one who is going to offer the sacrifice , namely the owner of the sacrificial animal. 
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“With regard to the family of the one who is going to offer the sacrifice, they are not subject to any obligations, and it is not forbidden for them to remove anything from their hair or nails, according to the sounder of the two scholarly views. Rather the ruling applies only to the one who is going to offer the sacrifice , the one who has bought the sacrificial animal from his own wealth.” (Fatawa Islamiyyah, 2/316) 
It says in Fatawa al-Lajnah al-Daimah (11/397): 
“It is prescribed for the one who wants to offer a sacrifice, once the new moon of Dhul Hijjah appears, not to remove anything from his hair, nails or skin , until he has offered the sacrifice. 
Umm Salamah (may Allah be pleased with her) narrated that the Messenger of Allah (peace and blessings of Allah be upon him) said: “When you see the new moon of Dhul Hijjah , if any one of you wants to offer a sacrifice, let him leave his hair and nails alone.”  (Narrated by the group except al-Bukhari)
A version narrated by Abu Dawud (2791) and Muslim (1977) says: “Whoever has an animal to slaughter , when the new moon of Dhul Hijjah appears, let him not remove anything from his hair or nails until he has offered the sacrifice.” This applies whether he is going to slaughter the sacrifice himself or he has appointed someone else to do it; but with regard to those on whose behalf the sacrifice is being offered [i.e., his family etc], that is not prescribed for them, because there is no report to that effect.” 
Shaykh Ibn ‘Uthaymin said in al-Sharh al-Mumti’ (7/530): 
“For the person on whose behalf the sacrifice is offered, there is no blame on him if he removes anything from his hair or nails. The evidence for that is as follows: 

This is the apparent meaning of the hadith, which indicates that the prohibition applies only to the one who is going to offer the sacrifice. Based on this, the prohibition applies only to the head of the household, not to the members of his family, because the Prophet (peace and blessings of Allah be upon him) connected the ruling to the one who is going to offer the sacrifice, so what is understood is that this ruling does not apply to those on whose behalf the sacrifice is offered. 
The Prophet (peace and blessings of Allah be upon him) used to offer the sacrifice on behalf of his household and it is not narrated that he said to them, “Do not remove anything from your hair or nails or skin.” If that had been forbidden for them, the Prophet (peace and blessings of Allah be upon him) would have told them not to do it. This view is the more correct opinion.”

And Allah knows best.