Is it Islamically permissible for a divorced woman to dispose of her ex-husband's money that is in her possession to spend on their children if he refrains from supporting them? And is she entitled to keep this money in exchange for their maintenance, or must she return it to him?

Your spending of the husband's money on his children is permissible as long as it is within reasonable limits, and you are not obligated to return the money unless it exceeds the obligatory maintenance. Your going out with the husband's permission necessitates his provision for you. However, if you go out without his permission, there is a difference of opinion among scholars regarding whether the maintenance of a pregnant woman is forfeited due to her disobedience or not. It is advisable for wise people to intervene to reconcile between the spouses.