Is the questioner's action of refusing his sister's departure to live in her brother's house with a non-mahram man who does not pray and drinks alcohol considered a religious error? Does he have the right to prevent them, and what is the responsibility of each party in this matter?

It is permissible for a sister to travel and reside in her brother's accommodation if the place is spacious, has multiple rooms and facilities, and her brother is able to protect his sister from intermingling and seclusion. However, it appears from the question that it is not permissible for the sister to travel to reside with her brother, due to a prior acquaintance between the sister and the man, which encourages a relaxed attitude in the relationship, especially if the man is weak in religious commitment.