The central conflict of this story is Kit's conflict against herself. She is the protagonist of the story, so it is her tale. Her problem is that she doesn't know how to fit into her new society. She is uncomfortable, lonely, and confused. She wants to live as she had Barbados, but Connecticut is a much different place with different rules. While the colony isn't perfect, it isn't the colony that has to change - it is Kit. She has to learn how to adjust to any environment. It is part of growing up, and this is a story about Kit growing up, learning what is important to her and learning how to be tolerant. Kit's maturing is made clear in the last chapter, as she happily accepts Nat's proposal and looks forward to a happy life.
For the other conflicts that Kit experiences, see the links below: