Is a mother obligated to pay the amount she promised her husband, from the money her children collected for her, after he stopped spending on her?

According to the majority of scholars, a promise is not legally binding. Therefore, your mother is not obligated to give your father the amount she promised him. Furthermore, the husband is not obligated to cover the expenses of his wife's treatment, according to the general consensus of scholars. The wife's service to her husband is obligatory according to the most authoritative opinion, so your mother is not permitted to cease serving your father. It is advisable to strive for reconciliation between your parents.