Is it permissible to refrain from giving the mother a monthly sum if she is extravagant with it, knowing that the father covers her needs and more?

We advise you to fear Allah. Then, counsel your mother gently and wisely by explaining the harms of extravagance and the frequenting of markets by women. If she does not benefit and you believe it is more likely that withholding money from her will improve her situation, then you may do so, and there is no blame upon you.