The women's role in the Puerto Rican culture is not expected to reach further than a homemaker. If you were young, then you must help with the chores around the house. Going out with friends was prohibited, unless you had the proper chaperone. Even at the age of 16, a young woman is highly protected. You may now understand why the father was so over protective and difficult to bare.
The women's role in America is much more different than Puerto Rico. Freedom is given and does not bound a woman to what a male allows. The respect is much higher. Females try to achieve higher standards in life, much more than just a homemaker. At the age of 16, a girl is most likely allowed to be with friends un-chaperoned.
The parents obey the Puerto Rican Culture because it is what they grew up with. They want their daughter to be raised the same way. This is shown because they enforce the same rules. The daughter wants to follow the American culture, but her family restricts her. When arguing with her father, she points out that they do not live in Puerto Rico anymore, it is Patterson, NJ. She uses examples such as the scenery outside to exploit the situation. The parents never seem to care.
So do you see the differences between the family. I agree with parents for a few reasons. They are teaching their daughter respect. She is also reading a lot, and developing an adventurous imagination along with a strong vocabulary. The one thing I disagree with is that the daughter is prevented from being with friends. Being with friends increases your social skills. In America these days, social skills are what you need to succeed. It does show that she did follow the correct path though. She is now a successful author writing about her past. Without her conflicts, she may not have been where she is today.