Is it permissible to give Zakat on wealth to one's sister and brother if part of the Zakat will be used to purchase something that benefits them and their parents who live with them?

It is permissible to give Zakat to a brother or sister if they are among those who are eligible for it; in fact, it is preferable. The parents' benefit from it does not prevent this, because the Zakat becomes their property after it is paid. One should not stop giving to the parents under the pretext that they benefit from their children's Zakat.