I believe that the confrontation about which you are asking occurred on the first day that Melba tried to attend Central High. As they approached the school, Melba and her mother found themselves "trapped by a violent mob". Trying not to attract attention, they attempted to ease their way out of their position, but they were noticed by a white man who grabbed Melba's sleeve. While the man was momentarily distracted, Melba "somehow managed to scramble away". Mother took Melba's arm as a commotion began building, and the two "moved fast, sometimes crouching to avoid attracting more attention".
Melba and her mother managed to get away from the center of the crowd, but a man and some others began to chase them. As their pursuers gained on them, Melba's mother tossed the keys to Melba and commanded her to get to the car, even if she had to leave her mother behind. Melba refused, and her mother, for the first time in her life, slapped her. Still, Melba would not leave her mother there, and, even though her mother's pace was slowing as the men behind them were gaining ground, Melba reached back to take her mother's arm and press on. The men chasing them were joined by another man who was carrying a rope, and one of the pursuers came close enough to Mother to tug at her blouse, ripping the fabric. Another man swung at Melba with a large tree branch; just when it seemed that there was no hope, the car came into view. Melba, running faster than she had ever run before, unlocked the door, jumped into the car, and swung open the passenger door for her mother. As her mother leaped into the car just in time, Melba revved the engine and sped down the street, while one of the men caught up and pounded on the hood with his fist and another threw a brick at the windshield.
It is clear that Melba was justified in defying her mother's order to leave her behind. The crowd was whipped up into a frenzy, wielding rope and weapons meant to seriously hurt and maybe even kill them. There is no doubt that, had Melba not acted as she did in defiance of her mother's directive, her mother would have undoubtedly been severely beaten or worse (Chapter 5).