By the will of God, I intend to perform the obligatory hajj this year. Will it suffice to slaughter there or must my family, who will remain here, offer a sacrifice as well?

If you are going on hajj tamattu' or qiran, then it is obligatory to slaughter a hady in al-Haram (Mecca, Mina, Muzdalifa or in any of the sites called al-Haram). This is what is obligatory, but what is recommended for you to do (you are rewarded for performing it but refraining from performing it entails no consequences), is to slaughter any kind of livestock animal and distribute its meat in charity among the poor of al-Haram and the surrounding areas.

It is likewise recommended to offer a sacrifice because, according to the opinion of the majority of scholars, sacrificial animals are recommended for both a pilgrim and others though it is not associated with al-Haram. Therefore, you may slaughter in al-Haram, Egypt or any other place where Muslims are in need such as Palestine, Somalia or elsewhere.