What is the ruling regarding a husband remaining with his wife who does not wear the hijab, and what are the consequences if she insists on her stance?

You erred by marrying a woman who does not wear the hijab, while the Prophet urged marrying a religious woman. Your wife must obey you regarding the hijab, and her statement "I am not convinced" is dangerous, because a believer has no choice when Allah and His Messenger have decreed a matter. You must compel her to wear the hijab. If she insists [on not wearing it] and you are unable to compel her, then it is better to divorce her, and some scholars have made it obligatory. Take the path of wisdom to reform her by every means, and help her strengthen her connection with her Lord by accompanying righteous women, listening to admonitions, and reciting the Quran. Persist in supplicating for her guidance.