Is it permissible for a non-working wife to donate a portion of the money her husband allocates for her personal needs and household necessities, on behalf of her deceased relatives, if her husband does not object to her donating her own money? And is this money considered a gift to her, over which she has full disposal?

This money remains the property of the husband, and the wife is his agent in spending from it on herself and her home. It is permissible for her to give charity from it with his general permission, or with a small amount that is customary, provided that it does not harm the husband or the household expenses. If the wife has a right to this money, then she may give charity from it as she wishes.