As this is a personal task, we cannot provide an essay for you. However, we can provide an initial analysis of the story that can help as guidance for your work.
In the story "Two Kinds," we witness the conflict that exists between Jing-mei and her mother. Jing-mei was born in the United States, but her mother came from China, and this creates a difficult cultural conflict between the two. While Jing-mei has dreams that could be characterized as more "American" (such as being a Chinese Shirley Temple), her mother wants her to follow her instructions and be more traditionally successful.
One meaning of the "two kinds" idea is that of the conflict between the kind of daughter Jing-mei is meant to be and the daughter that she actually is. However, another meaning becomes obvious towards the end of the story. As she finds the two halves of the song ("Pleading Child" and "Perfectly Contented"), Jing-mei realizes that she is also two different kinds of person, who are not necessarily in conflict, but can reconcile. The two parts of her are as much united and complementary as the two parts of the song.
