If you are just looking at Chapter 2, I would say that the relationship between these two is very poor.
Formally, their relationship is that of teacher to student. This means that Miss Caroline should be the superior. She shows that she has this kind of formal authority by hitting Scout's hand and making her stand in the corner.
But in some ways, Scout is the real teacher in this relationship. She is actually trying to help Miss Caroline learn things about Maycomb society. And she shows the teacher more sympathy than the teacher shows her.
Miss Caroline and Scout had a student-teacher relationship in chapter two of To Kill a Mockingbird. Their relationship was a tumultuous one, as they did not understand one another. On the first day of school, before the day was even close to being over, Miss Caroline "hauled [Scout] up to the front of the room and patted the palm of [her] hand with a ruler, then made [her] stand in the corner until noon." Miss Caroline thought that Scout was being impertinent and a liar because the child told her that no one taught her to read. Miss Caroline did not understand that Scout was telling the truth, and Scout did not understand why Miss Caroline would treat her so. Later, Scout tried to explain to her teacher that she was making Walter Cunningham feel ashamed by offering to loan him money for lunch. Miss Caroline thought that Scout was trying to cause trouble, and this was when she finally decided to punish her.
Miss Caroline was a young teacher with little experience. As Scout left the classroom, she saw the woman "bury her head in her arms." Scout admitted that she "would have felt sorry for her" if she had not treated her so badly.