why does she push June to become a prodigy? how does she much later revise this?

Suyuan believes in the American Dream. She thinks that with talent and hard work, any obstacle can be overcome despite background or ethnicity. This is why she wanted her daughter to become a prodigy or American success story. In the end Suyuan has failed to reunite her daughters so it is then up to Jing-mei to fulfill her "long-cherished wish" of reuniting with them in China. I think she sees that spirit and determination in her daughter that changes her view.