As for many people living through the Great Depression, life is extremely tough for Lizabeth and her family. Lizabeth's father is out of work, like millions of other people across the country. Unsure when, if ever, he'll get a job that will allow him to provide for his family, he is plunged into a pit of despair and anguish that causes him to break down and cry.
Lizabeth has never heard a grown man cry before and, as one can imagine, she's deeply upset by this new and unpleasant experience. To a large extent, Lizabeth's happiness is bound up with that of her father. If he's happy, then all is well. But if he's not—and he most certainly isn't, on account of his unemployment—then she too will be unhappy.
This creates a problem for Lizabeth. She may be angry, hurt, and upset, but she cannot very well take out her frustration against the economic system that put her old man out of a job. So instead, she takes it out on Miss Lottie by destroying her marigolds.
As well as being a wanton act of vandalism, Lizabeth's actions are completely unfair. It's not Miss Lottie's fault that Lizabeth's dad's out of work. Nor is Miss Lottie standing in the way of her happiness. But as this is the only way that Lizabeth can deal with her anger and frustration at what unemployment has done to her father, she engages in an act of destruction that reveals her deep unhappiness at her situation in life.