Jing-Mei's mother wants her daughter to retain the customs and traditional female roles particular to Chinese culture. She wants to mold Jing-Mei in this way, but also with just enough American influence to promote and encourage Jing-Mei to become a typical American success story. There is nothing wrong with trying to instill an awareness of her old and new cultural influences in a child, but Jing-Mei's mother is too controlling. This idea of molding Jing-Mei clashes with the American ideals of individuality and self-reliance.
Growing up in America, Jing-Mei has more of that cultural influence of individuality than her mother does. She doesn't resent her mother for encouraging her to succeed. She resents her mother for controlling her life and attempting to mold her (Jing-Mei's) personality. Jing-Mei is making the shift from obedient daughter to a more self-motivated young woman. This is the shift from one "kind" to another. When her mother gives her an ultimatum, Jing-Mei rebels:
"Only two kinds of daughters," she shouted in Chinese. "Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"
"Then I wish I weren't your daughter, I wish you weren't my mother," I shouted.
It sounds quite cruel, but Jing-Mei, in that moment, feels like she has to rebel against this ultimatum.