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. The prohibition to remove anything from hair or nails applies only to the head of the household, not to the members of his family.

If you and your brother live in separate houses, then it is prescribed for you to offer the sacrifice on behalf of yourself and the members of your household, and your brother should offer the sacrifice on behalf of himself and his household. The sacrifice offered by your mother on behalf of herself and the members of her household is not sufficient for you and your brother.