Is expiation obligatory upon the driver who does not possess a driving license and had an accident, and his brother took his place and swore an oath that was not true? And is expiation obligatory upon the brother, knowing that both parties are married and have children?

The act of a brother impersonating his brother and writing his name instead of his on official documents is considered lying and forgery, requiring repentance from both parties. If the brother falsely swore that he was the driver of the car, this is a "yamin ghamus" (a false oath taken deliberately to seize a right or avoid an obligation) and a major sin. Its حرمة (sacredness/prohibition) increases if sworn upon the Qur'an, and it necessitates sincere repentance ("tawba nasuh"), with a recommended expiation for the oath. However, if he swore an oath about the details of the accident without mentioning who was driving the car, and what he said was consistent with reality, then there is no blame upon him.