Is the sacrifice of a brother sufficient on behalf of his brother who lives in a separate apartment in his house, and on behalf of his two adult sons (16 and 19 years old), knowing that they spend on themselves?

The permissibility of sharing in the reward of the sacrifice (udhiyah) is conditional on the sacrificer financially providing for those he includes, this being the view of the Maliki school and one opinion among the Shafi’is. Accordingly, your brother's sacrifice does not suffice for you as long as he does not provide for you. Some scholars have held that it is permissible to share in the reward if the sacrificer intends it, without requiring cohabitation or financial provision.