What does Liberty teach the narrator about both personal and political freedom in Julia Alvarez's short story?

In Julia Alvarez's story "Liberty," the puppy's name deliberately evokes the concept of freedom that the narrator's father associates with the United States. The narrator is a girl too young to understand these abstract ideas. For her, the puppy is just a puppy, and she is upset that they have to leave him behind when they abruptly leave the Dominican Republic.
When Liberty runs away, the narrator is introduced to the secrecy and surveillance that represents the lack of liberty in her own country; she encounters the repression of the state apparatus by way of the two men lurking outside and experiences the fear of imposed silence. However, she cannot solely associate their new life with the concept of freedom. Instead, she focuses on unjust rules and regulations that their transition will impose on them, represented by the immigration barrier that will not allow the puppy into the country.
Her attachment to her own country and culture are symbolized in her efforts to send the dog away; he will gain an imperfect freedom that also means lack of protection.