The main conflict in “Two Kinds” is between mother and daughter (character vs. character). Jing-mei is not a child prodigy, and her mother wants her to be. Jing-mei, the main character, wants to please her mother but she wants to be herself too.
Jing-mei’s mother wants more than anything to be able to praise her daughter to her friends. She wants Jing-mei to be some kind of prodigy, just as Waverly is a chess champion.
Unfortunately, Jing-mei does not have the talent or dedication to become a prodigy. The dream is not really Jing-mei’s. She wants to make her mother happy, but she also wants to be herself. She wants her mother to appreciate and love her for who she is. Ultimately, her lack of distinct accomplishment helps maintain the rift between mother and daughter.