What is the ruling of the Sharia regarding the mother of the husband always demanding a lot of money, despite her not needing it, and despite the wife's knowledge of the rights of parents?

The husband must give his mother whatever money she requests, within reason, as long as she does not spend it in an unlawful way. This is part of being dutiful to her, which Allah has commanded and encouraged. The wife has no right to object to this, as long as the husband is fulfilling his duty of providing for her and their children.