Is it permissible for a man to give his divorced daughter and her children from his Zakat money, knowing that her ex-husband does not provide for them?

If a man does not provide for his divorced, poor daughter, then it is permissible for him to give her from his Zakat. However, if he does provide for her and her children, then it is not permissible for him to give her from his Zakat, because it would be as if he is paying Zakat to himself.