What is the correct course of action regarding moving in with the husband's mother, who drinks alcohol, smokes, and associates with men, knowing that the girl's family is angry due to her adherence to her religion?

It is not permissible for a Muslim to reside in a disbelieving country except out of necessity or need, and we do not believe there is a necessity for your studies there. Your stay with your aunts—in the situation you described—poses a great danger to you. Therefore, it is more appropriate for you to travel to your husband and reside with him to safeguard your religion and honor. There is no harm in your traveling without a mahram if the situation necessitates it. Strive to advise your aunts, and do not be concerned by your family's dislike of you because of your religion. Remember the hadith: "Whoever seeks Allah's pleasure despite people's displeasure, Allah will suffice him against people's burden. And whoever seeks people's pleasure despite Allah's displeasure, Allah will entrust him to people."