Is it permissible for the father to give Zakat on his money to the children he had with another wife, who live with their wealthy maternal grandfather, in the event that the father does not spend on them?

The father is obligated to provide for his children if he is able. If he refuses to provide while capable, he is disobedient and sinful. If their maternal grandfather is providing for them and is well-off, then it is not permissible to give them Zakat because they do not qualify as poor.