Is a husband obligated to provide his wife with a profitable venture if he is protective of her and her basic expenses are sufficient, so that she may spend from its proceeds on her mother or on permissible hobbies that the husband considers frivolous?

The husband is not legally obligated to finance a commercial project for his wife. Rather, his obligation is to provide for her sufficiently. It is preferable for a woman to remain in her home to manage her family's affairs, as stated in the Almighty's saying: "And stay in your homes." If the husband can finance a project managed by his wife from home, it is a good thing, especially if she is in need of money.