How can the story "Two Kinds" be misunderstood?

There are, of course, many ways to misunderstand any short story, and in this regard, “Two Kinds” is no exception. But the story does end with the narrator experiencing an epiphany, and it is an epiphany that clarifies a misunderstanding that she has long had. Because of that, this answer will focus on the narrator’s own misunderstanding, and how it might relate to the reader’s own.
As the title suggests, the short story sets up a series of oppositions. The main one is introduced by the mother, who tells her daughter that there are only two kinds of daughters:

"Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"


But in the final moment, we realize that this is not the case. Looking at the sheet music, the narrator experiences an epiphany:

And for the first time, or so it seemed, I noticed the piece on the right-hand side. It was called "Perfectly Contented." I tried to play this one as well. It had a lighter melody but with the same flowing rhythm and turned out to be quite easy. "Pleading Child" was shorter but slower; "Perfectly Contented" was longer but faster. And after I had played them both a few times, I realized they were two halves of the same song.

The narrator realizes that the mother was wrong; the binary relationship between the two kinds of daughter can be deconstructed, and that they actually coexist inside one another. This moment also helps the narrator realize why her mother kept the piano for her: although she did not become a piano-playing prodigy, her mother still saw her as a success. As the narrator explains, “after that, every time I saw it in my parents' living room, standing in front of the bay window, it made me feel proud, as if it were a shiny trophy that I had won back.”
These two intersecting epiphanies corrects the narrator’s—and potentially the reader’s—misunderstanding: although the mother is disappointed with the daughter’s performance and behavior, she is not disappointed in the daughter as a piano player or a person.