Am I obligated to go on Hajj with the money I possess, knowing that my mother might get angry, and I might not get another chance to perform Hajj, or should I save the money to buy my mother a car?

The Hajj is one of the pillars of Islam. It is not permissible for one who is able to delay it or hesitate in performing it. There is no obedience to anyone in disobedience to Allah; therefore, it is not permissible to please one's mother by disobeying Allah.