In a dialectical journal, you are to write quotes from the text as you read, and personally respond to those quotes. Keep in mind that "dialogue" (as in, characters speaking) is not what is meant by "quote." *My students are often confused by this. Rather, a quote is any line from the text that you write down and respond to. The quote can be dialogue, but does not have to be.
I assume from your question that this project was given with a specific set of instructions which dictate different types of quotes on which to respond. My best guess (as a teacher) is that quotes which are "stated directly toward" Jeanette Walls, means things which were, in fact, said to her (in this case, dialogue) as a child. The book is written in first person, which means all of the dialogue comes from the author's memory. Likely, your teacher wants you to look for some of the key things one of her parents said to her as a child that stuck with her (as evidenced by the fact that she includes them in her book).
As you read, if you find yourself cringing at some of the things her mother and father say to her, you might jot them down and write a personal reaction. This should satisfy the "directly stated toward" requirement.