Is it permissible not to pay the monthly fees for the nursery, after the mother swore an oath to that effect because her son was beaten by a worker at the nursery?

It is not permissible for an oath by God to prevent the fulfillment of a right owed to another. Rather, one must break the oath, fulfill the right, and offer expiation for it. Ibn Qudamah said: "If the oath was to commit something forbidden or to neglect an obligation, then breaking it is obligatory." Accordingly, the due fees must be paid, and expiation for the oath must be offered.