Is it permissible for a wife to allocate a portion of her Zakat money to spend on her children, even though her husband is capable of spending on them?

The maintenance of children is obligatory upon their father according to the Qur’an, Sunnah, and scholarly consensus. If the father is providing sufficiently for his children through his own expenditure, then it is not permissible for the wife to spend on them from her Zakat, because Zakat has specific, legally defined recipients.