Esmeralda was a one-eyed cat, that, when a tornado ripped the roof off of the McDonald's dairy barn, was the only animal who was not harmed in any way. She remained intact.
Patty sees herself as similar to the cat. The cat is disfigured and ugly, but strong, and Patty often mentions how little she thinks of her looks, but the reader can see how strong her spirit is.
Her father is representative of the tornado. He will come at her in a whirlwind of anger, he will try to tear her apart, and he will try to break her. But she says that, no matter what he says or does, she will remain intact, just like that cat. She simply knows that no matter how strong her father - the tornado - may think he is, she is stronger and has a stronger will to survive, like Esmeralda, the one-eyed cat. She states that, because of this strength and will to survive, her father was forced to respect her.
"The new ingredient wasn’t love, it wasn’t as good. It was, I guess, respect. Respect for a person who he’s incapable of destroying."