Is it permissible to retrieve the remaining money from the father without his knowledge, after he refused to return the price of the car that was sold to help the brother, knowing that he does not treat his children justly?

We understand from the question that your brother asked you for money, so you sold your car and lent him its price. Then your father promised to buy you a car but did not fulfill his promise. If this is correct, then it is not permissible for you to take anything from your father's money without his knowledge and consent, under the pretext that he promised you and did not fulfill it. This is because your brother is responsible for repaying the loan, and your father is not obligated to pay his son's debt. Fulfilling a promise is not obligatory according to the majority of scholars, and your father's right over you is immense, even if he prefers some children over others.