How we cite our quotes:
Quote #1
The grandmother didn't want to go to Florida. She wanted to visit some of her connections in east Tennessee and she was seizing at every chance to change Bailey's mind. (1)
We're given the indication as early as the second line of the story that the grandmother's determined to get what she wants, and will do whatever she can to do it. This already suggests what the grandmother says might have an ulterior motive.
Quote #2
"Now look here, Bailey," [the grandmother] said, "see here, read this," and she stood with one hand on her thin hip and the other rattling the newspaper at his bald head. "Here this fellow that calls himself The Misfit is aloose from the Federal Pen and headed toward Florida and you read here what it says he did to these people. Just you read it. I wouldn't take my children in any direction with a criminal like that aloose in it. I couldn't answer to my conscience if I did." (1)
The grandmother first brings up The Misfit not out of genuine fear, but instead to guilt or scare her son into taking the family to Tennessee instead of Florida. (She wants to go to Tennessee to visit relatives.) It's also notable that the grandmother uses moral language – appealing to conscience – as a further means of manipulation.
Quote #3
[The grandmother] had her big black valise that looked like the head of a hippopotamus in one corner, and underneath it she was hiding a basket with Pitty Sing, the cat, in it. She didn't intend for the cat to be left alone in the house for three days because he would miss her too much and she was afraid he might brush against one of her gas burners and accidentally asphyxiate himself. Her son, Bailey, didn't like to arrive at a motel with a cat. (10)
The grandmother hides her cat from the rest of the family. Its clear that she does what she wants without consideration to others. If she wants to bring the cat, she will, regardless of the opposition. This blurb happens to also be a funny moment in the story.