The change in the narrator is shown by her act of driving away Liberty, her dog, that she loves so much and has previously described as "a double of herself." Notice how at the end of the story, to save Liberty from the "men in sunglasses," she is forced to convince Liberty that he is no longer wanted:
I kick him, softly at first, but then, when he ckeeps tagging behind me, I kick him hard.
Of course, it is important to realise how Liberty the dog functions as a symbol of the liberty that the narrator and her family are hoping to gain by fleeing to the United States. Liberty requires sacrifices, and in order to find sanctuary elsewhere, the narrator and her family must sacrifice their home and possessions. The change in the narrator is that she has learned the necessity of this and does what she needs to do in spite of the love she has for her dog--and symbolically of her home and possessions. Note how she shows awareness of this at the end of the story:
He will beat me to the United States is what I am thinking as I head back to the house. I will find Liberty there, like Tia Mimi says. But I already sense it is a different kind of liberty my aunt means. All I can do is hope that when we come back--as Mami has promised we will--my Liberty will be waiting for me here.
Thus this excellent short story presents us with a young girl who is forced to mature because of the loss she must undergo in order to paradoxically gain liberty by losing her own Liberty.