Is the mother obligated to pay Zakat on money she secretly saved for her daughter, without the father's knowledge, if the money reaches the threshold for Zakat, in order to prevent the father from squandering it?

A mother is not permitted to save money from her husband's wealth unless he gives her permission. She must return the money to him or ask him to gift it to her. It is not permissible to pay zakat on money without the owner's knowledge, because intention is a condition for the validity of zakat.