What is the legitimate Islamic method that a husband should follow with his wife and her family regarding issues of clothing and mixing (with the opposite sex), especially after the wife began to backtrack on her previous commitment, and what is the ruling on a wife refusing to wear the jilbab in front of her mother when her husband requests it?

Islam encourages women to purify themselves and to wear the hijab, which protects them and shields them from degradation, which corrupts society. If a woman is in front of non-mahram men, she must wear the hijab. However, in front of her mahrams or other women, she may wear whatever covers her 'awrah. The Muslim woman receives this duty as an act of worship. If a woman falls short, her guardian commands her to wear the hijab, and the husband is responsible for wisely commanding his wife to wear the hijab. The hijab is obligatory in front of non-mahram men, not in front of women or mahrams. The wife must obey Allah and her husband in what is good.