Is it permissible for my mother to give Zakat money to my widowed sister, who has three children and lives with my mother?

A mother is not permitted to give her Zakat to her daughter if the daughter's maintenance is obligatory upon the mother and the mother is wealthy, unless the Zakat is for repaying a debt incurred by the daughter that is unrelated to her maintenance. It is permissible to give Zakat to deserving relatives if the Zakat payer is unable to support them or to repay their debts, even if they are among those whose maintenance is obligatory upon him, provided that the debt is not due to maintenance that is obligatory upon the Zakat payer, in order to avoid circumvention.