Is it permissible to give Zakat to my widowed aunt who has two minor children, one of whom has special needs, and she has no one to support her except for a small allowance, and she lives in rented accommodation in Jordan, and she has a bank balance of eleven thousand Jordanian Dinars from previous Zakat payments?

Your relative should not be given zakat (definition) if what she possesses suffices her and her children for one year, because zakat is an annual obligation, and whoever possesses what suffices him for a year is considered wealthy in the context of zakat.

However, if what she has does not suffice her, then you may give her zakat, and she has more right to your zakat than a stranger, due to the Prophet's (peace and blessings be upon him) saying: "Charity given to the poor is a single charity, but given to a relative, it is two: charity and maintaining kinship ties."