Answer:
The central conflict in Amy Tan's Two kinds is between the narrator and her mother. An immigrant from China who has lost everything, the mother is a firm believer of the American dream, that in American anyone could become someone important, successful, a prodigy. So she pushes her daughter in the widest variety of activities, so she can become a prodigy, the central one playing the piano. But the daughter, the narrator, doesn't want to be a prodigy, she just wants to be her. So she resists her mother attempts and doesn't really learn to play the piano, doesn't even give it a chance, despite she enjoys it. Her mother just wants her to practice, to make someone out of her, that she learn something, even if she doesn't become a prodigy. So when the daughter fails at a recital, the mother feels disappointed and ashamed. They have a big fight and the daughter quits the piano, the mother stops pushing her into things she doesn't want to do.
Many years go by, the mother dies and the daughter/narrator sits in front of the piano after a long time. The partitures of the failed recital are there and she plays it, noting that she only played one part of it, "pleading child", missing the "perfectly contented" part, and how one makes no sense without the other. So she kind of makes amends with her mother.