An essay that emphasizes culture and history should look at the larger context in which the individual story is set. The suggested themes of mother–daughter relationship and the daughter’s role both focus on the characters, while a consideration of ethnic identity is more closely connected to the larger cultural and historic issues. While “Hispanic” does apply to US residents from the Dominican Republic, it is probably too broad to usefully generate a thesis that is specific to one short story.
It could be helpful to learn about the time period in which Junot Diaz situates the story. What important historic events were happening in the Dominican Republic? What was US immigration policy toward Dominicans at that time? Where were the largest Dominican American communities in the United States? One could then connect those events and trends to the situation in which the protagonist found herself when her mother sent her from the United States to live in the island republic.