The answer is the third option: The conflict is external and takes place between a mother and her daugther.The theme in "Two Kinds" is the conflict between two kinds of women.
In the short story "Two Kinds," Amy Tan tells us about the confrontation of cultures between a first-generation Chinese-American daughter, Jing-mei, and her mother, Suyan, a Chinese immigrant. Suyan is sure that Jing-mei can become an exceptional girl if she only works hard enough. Jing-mei always falls short of her mother's expectations and decides that she would become a prodigy by constantly refusing to do what her mother wishes.