Is it obligatory to offer another sacrifice during Hajj if the family of the pilgrim has already offered a sacrifice on his behalf?

The Udhiyah (sacrifice) is not obligatory for the pilgrim, nor is it legislated for him to slaughter it in Makkah. Rather, what is obligatory and legislated for him is the Hady (sacrificial animal offered during Hajj). If he performs Hajj as a Mutamatti' (combining 'Umrah and Hajj) or a Qaarin (combining 'Umrah and Hajj with one Ihram), the Hady becomes obligatory upon him. This Hady is an animal sacrifice that must meet the same conditions as the Udhiyah, based on the Almighty's saying: "But whoever performs 'Umrah in conjunction with the Hajj [i.e., Tamattu'] then [he must offer] what can be obtained with ease of the Hady. But if he cannot find [one], then a fast of three days during Hajj and seven when you have returned [home]. Those are ten complete [days]." (Qur'an 2:196). However, if he performs Hajj as a Mufrid (Hajj only), the Hady is not obligatory for him, but it is recommended for him to offer it voluntarily. If the pilgrim leaves his family in his homeland, it is legislated for him to leave them money to perform the Udhiyah on his behalf.