What details throughout the book show that Lyddie is proud?
I think that the early chapters of the book do a nice job of showing the reader that Lyddie is a proud and determined girl. I think a good early example is her determination to continue taking care of the farm through the winter despite her mom leaving. Lyddie is too proud to just leave the farm and let it go to waste. She and Charlie do quite well with the responsibilities as well too; nevertheless, they are both sold into indentured servitude.
While Lyddie is worked to the ground by Mrs. Cutler, Lyddie is proud enough to not give up and cower from Mrs. Cutler. At one point Lyddie thinks the following line.
Mrs. Cutler watched Lyddie like a barn cat on a sparrow, but Lyddie was determined not to give her cause for complaint.
Lyddie is proud of her ability to work and work hard. That pride continues throughout the story. She is determined to learn how to operate her own loom. It pays off, and she quickly becomes one of the strongest factory girls. That pride in her accomplishments leads to Lyddie's dismissal of Brigid's initial efforts. Lyddie believes that she is too effective and talented to waste her time and efforts on teaching a girl like Brigid. That's Lyddie's pride having a negative impact on her and the people around her.