What is the legitimate Islamic way to deal with a wife who withholds herself from her husband and demands that he curse another girl, and taunts him about not spending on her, while the husband suffers from overwhelming financial hardship and sexual deprivation?

The Shariah has granted the husband guardianship over his wife and obligated her to obey him in what is good, including responding to his call to bed. If she refuses without a valid excuse, she is considered disobedient (nashiz). What you mentioned about your wife's request to insult a girl, and her refusal to intimacy because you did not fulfill her request, is a sign of her foolishness and lack of wisdom, and it is not a Sharia-sanctioned excuse for her refusal. However, her refusal to intimacy due to your failure to spend on her is her right, as jurists have stipulated the permissibility of this if the husband is unable to provide maintenance or refuses to provide the obligatory maintenance. We advise you to strive for reconciliation, but if it is not achieved, then consider divorcing her and marrying someone else for your overwhelming benefit. If there is no other option but patience, then fear Allah, be patient, and seek help in maintaining chastity through fasting and keeping good company. Beware of entering suspicious websites, as they are a disease, not a cure.