What is the ruling on continuing a marriage to a wife who does not wear the hijab and believes it is obligatory only for the wives of the Prophet, given existing marital disagreements and quarrels?

You must be a helper to your wife, not an assistant to Satan against her. It is recommended to teach her matters of her religion, such as prayer and hijab, to treat her kindly and with beneficence, to control anger, to be a role model for her in obedience, and to deal with her gently and kindly. For the fear of Allah protects from marital problems. If the wife does not pray regularly or goes out unveiled, she is disobedient (nashiz), and the husband has the right to treat her as such. The wife does not have the right to demand a divorce merely because the man marries another woman, provided he has not fallen short in her legitimate rights.