What should I do regarding my husband's insistence on not financially supporting our eldest daughter after she was expelled from the house because of her relationship with her cousin, and his threat to end our marital relationship if I spend from his money on her, knowing that I do not work and have no income of my own?

The husband has acted improperly by refusing to provide for his daughter, and this is an injustice to her, to him, and to his children, and it is corrupting for his daughter. His statement, "If you spend a single penny of my money on her, you will be living with me in sin," requires understanding his intention. If it was a promise of prohibition, then nothing is necessitated by breaking it, and you can spend on the daughter from his money without his knowledge. However, if he intended to make the prohibition contingent upon your spending from his money, then if you spend, what he intended, whether it be divorce, ẓihār, or an oath, will occur. We advise you to try to reach an understanding with him and explain that his action violates Islamic law. You can also involve some righteous people as mediators. Otherwise, you should refer the matter to the judiciary.