What is the primary conflict occurring in this excerpt? --- One day after we left a shop I said under my breath, “I wish you wouldn’t do...

This is a great question, as it gets to the heart of the story. The conflict here is twofold and it is hard to determine what is more primary.

First, we see a conflict between mother and daughter.  The mother here wants to boast about her daughter.  This gives her a sense of pride.  Many parents are like this.  The problem is that Waverly wants to be independent.  She does not want to be seen as a daughter of someone.  She wants to be seen as Waverly. Hence, the conflict is one of independence.

Second, we also see a clashing of cultures.  In an Asian culture, individualism is not prized too much.  What is more important is the family. This is where Waverly's mother is coming from. However, Waverly is coming from an American point of view.  So, we see a conflict between traditional Chinese culture and American individualism.