In Amy Tan's Joy Luck Club, Suyuan's belief in American Culture is similar to the other Chinese mothers:

You could be anything you wanted in America (141).

Suyuan and the other mothers want the best of both worlds, a hybrid identity for their American-born daughters: freedom (American) and traditional values (Chinese).

Lindo Jong echoes this belief:

I wanted my children to have the best combination: American circumstances and Chinese character. How could I know these two things do not mix?

The mothers become disappointed in their daughters when the girls exhibit more freedom, which they see as rebellion to traditional Chinese values.  They believe their daughters are spoiled in American and ashamed of their mothers and heritage.

And, after seeing my mother's disappointed face once again, something inside of me began to die. I hated the tests, the raised hopes and failed expectations. Before going to bed that night, I looked in the mirror above the bathroom sink and when I saw only my face staring back--and that it would always be this ordinary face--I began to cry. Such a sad, ugly girl! I made high-pitched noises like a crazed animal, trying to scratch out the face in the mirror.

So says Enotes:

Suyuan’s declaration to Jing-mei, “You can be best anything,” reveals her appreciation of the opportunities available in America. Jing-mei shares her mother’s enthusiasm at first, believing that her prodigy side, symbolized by her Peter Pan haircut, will be perfect. As she fails test after test, however, she says, “I hated . . . the raised hopes and failed expectations.” Frustrated, she quits trying, and eventually so does her mother. Jing-mei says, “At last she was beginning to give up hope.”

The story is filled with duality.  Here, Jing-mei accepts hybrid identity:

And then I saw what seemed to be the prodigy side of me--because I had never seen that face before. I looked at my reflection, blinking so I could see more clearly. The girl staring back at me was angry, powerful. This girl and I were the same. I had new thoughts, wilful thoughts, or rather thoughts filled with lots of won'ts. I won't let her change me, I promised myself, I won't be what I'm not (144).

In Amy Tan's "Two Kinds," the mother embraces the American Dream and tries to turn her daughter into a celebrity of some kind.  She doesn't care what kind, she just wants a child prodigy for a daughter.  Her stern and uncompromising parenting methods result in the destruction of her relationship with her daughter, and achieve the opposite effects from her daughter.

The mother isn't satisfied with just raising a normal child, she has to have a prodigy, American style.  The mother basically sets impossible goals for her daughter based on what she sees on American TV.

Jing-Mei rebels against her oppressive mother by only pretending to practice piano, etc.  Her feelings for or against American culture are probably best described not by her embracing anything in particular, but by her rejection of what her mother presents as the Chinese model of a family.  For the mother, there is only the dichotomy of a child who obeys absolutely everything she is ordered to do, and one who doesn't.  The mother divides the world into two parts--those who do things her way, and those who don't.

Jing-Mei rejects this dichotomy, and thereby, I suppose, accepts American culture, if you view the situation in those terms.