When school bully Lavinia accuses Sara of making up "fairy stories" about Heaven, Sara primly tells her that no one knows what Heaven is really like, but unless Lavinia starts being kinder to people, she'll never find out – a fairly classy schoolgirl way of telling Lavinia to go to hell.
When Lottie asks Sara to tell her stories about the diamond mines, Lavinia snaps and says that she would like to slap Lottie. Sara rounds on her, proving that she dislikes Lavinia, too, but is still the better person.
"Well, I should like to slap you - but I don't want to slap you. At least, I both want to slap you - and I should like to slap you - but I won't slap you."
After Sara is left poor on Miss Minchin's hand, she keeps her on as a scullery maid and girl-for-all to get some use out of her. Sara is about to leave, when Miss Minchin stops her.
Keep in mind that at the time this took place, children simply did not speak this way. The idea of a child speaking up (whether or not she was correct) against an adult was not just rude, but unnatural. As Mrs Reid says in Jane Eyre, it was as if an animal were to speak and call you out for beating it. It fits with the view of Sara being regarded as a bit uncanny.
Sara has told the younger children the story of King Alfred getting hit by a neatherd's wife for burning some cakes and her shock at learning that she just assaulted her monarch. While she's smiling and thinking, Miss Minchin boxes her ears, just like it happened to Alfred. After Sara explains that she wondered what Miss Minchin would do if she learned that Sara was actually a real princess and could do whatever she wanted, she'd never dare to raise her hand against her. Miss Minchin demands that Sara apologize.
"I will beg your pardon for laughing, if it was rude, but I won't beg your pardon for thinking."
Upon learning that not only has Sara's wealth has been restored, but she's actually much, much richer than she was before, Miss Minchin tries to convince her to stay at the school as a parlor-boarder again, with all her old privileges reinstated. She even tries to convince Sara that it would be what Sara's father would have wanted. By the time she's finished, Sara's all but shaking with rage, but manages to tell Minchin calmly and firmly, "You know why I will not go home with you, Miss Minchin. You know quite well". Even in a situation where Sara has all the power over a woman who abused and mistreated her, she's still so far above Minchin that she won't humiliate her publicly by stating the reasons why she won't go back, something Miss Amelia points out most other children wouldn't do. Instead she puts Minchin in a position where she'll have to humiliate herself, either by admitting the truth and begging forgiveness, or by denying she knows why Sara won't stay, which everyone knows is untrue. (Minchin chooses to deny, proving once and for all what a craven coward she is.)
Ermengarde's announcement: "There WERE diamond mines. THERE WERE!" This is followed by her blurting out the full story to the entire school (doubly delicious, since now there's no way for Miss Minchin to keep it under wraps) and concluding, "And I'm going to visit her tomorrow so there!"
Miss Amelia ripping into her sister, to the point of hysterics. And Miss Minchin is actually impressed by Amelia.
