Is it permissible for a wife to dispose of money she saves with her husband's knowledge but without his explicit consent, or to take from his money without his knowledge, especially since part of his additional income is spent in her name and the names of her children, given his stinginess and refusal to purchase essential needs and gifts for her and their children?

It is the wife's right that her husband spend on her and their children according to what is customary, and the husband is rewarded for his spending. The wife is entrusted with her husband's money, and it is not permissible for her to take from it without his permission as long as he is spending according to what is customary. If the husband is stingy, then it is permissible for the wife to take what suffices her and her children according to what is customary, without his knowledge. What the husband saves for his wife is considered a gift, and the wife owns it and may dispose of it without his knowledge. Exchanging gifts between spouses is desirable as long as it does not violate the Shari'ah, with the caveat that celebrating birthdays and wedding anniversaries is not permissible. It is advised to be patient with the husband's behavior, to gently advise him, and to supplicate for him.