Is it a sin for the sister to refuse to return home and leave work, despite the long distance and renting a house, and is the position of the brother who refuses to complete his studies unless she returns correct?

Do not abandon your lawful studies. As for your sister's work, if it is permissible, and she finds a mahram to accompany her, and there is no harm or fitnah in her residence, then there is no objection to her working if she needs it for herself or her family. Otherwise, it is not permissible for her to work, and you should advise her gently and wisely.