"You wouldn't shoot a lady, would you?" the grandmother said and removed a clean handkerchief from her cuff and began to slap at her eyes with it. (86)
The grandmother now begins to convince The Misfit not to shoot her. Her first tactic is to appeal to being a lady. After all, everyone knows it's not proper to shoot ladies.
"You could be honest too if you'd only try," said the grandmother. "Think how wonderful it would be to settle down and live a comfortable life and not have to think about somebody chasing you all the time." (90)
The grandmother is again trying to work on The Misfit, this time by giving him the promise of a "respectable," and "comfortable" life. Her equation of "goodness" with the values of her social class is clear in what she says. None of this matters in her dealings with The Misfit, who she is woefully unequipped to manage.
[The grandmother] knew that Bailey would not be willing to lose any time looking at an old house, but the more she talked about it, the more she wanted to see it once again and find out if the little twin arbors were still standing. "There was a secret panel in this house," she said craftily, not telling the truth but wishing that she were, "and the story went that all the family silver was hidden in it when Sherman came through but it was never found . . ." (45)
Once the grandmother decides she wants to go to the house (out of nostalgia), she purposely says something false to ensure the children will cajole their dad into going there.
"Yes, it's a beautiful day," said the grandmother. "Listen," she said, "you shouldn't call yourself The Misfit because I know you're a good man at heart. I can just look at you and tell." (88)
We've already seen the grandmother call somebody (Red Sammy) a good man before, and it seemed pretty artificial. Now she seems to be hoping that she can either appeal to the "good man" in The Misfit, or convince him that he is enough of a "good man" to let her go. That she's sincere seems doubtful. We can't forget that the grandmother has already brought up The Misfit twice as a big, bad, scary man.
"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.
"Jesus!" the old lady cried. "You've got good blood! I know you wouldn't shoot a lady! I know you come from nice people! Pray! Jesus, you ought not to shoot a lady. I'll give you all the money I've got!" (131)
The grandmother offers The Misfit money. After he's already killed her family and told her he's not interested in stealing for gain, this attempt seems ridiculous. The Misfit doesn't take her seriously, and makes a joke in response. Although you could read the grandmother as trying another tactic of manipulation, you could also argue that she's reached such a state of desperation at this point that she's throwing out all of her old tactics at once. It now looks as if everything she said before was an attempt to keep herself alive.
"Bailey Boy!" the grandmother called in a tragic voice but she found she was looking at The Misfit squatting on the ground in front of her. "I just know you're a good man," she said desperately. "You're not a bit common!" (98)
Bailey's sent to be shot, and the grandmother quickly gets back to work on The Misfit. She doesn't beg for Bailey's life either. You could see this as evidence that all she really cares about is her own skin. Even when she despairingly calls out for Bailey, she's still looking at The Misfit. Then again, maybe she's genuinely traumatized by what's happening, and is reacting without thinking. Her attempt to appeal to The Misfit's better nature might be an instinctual move to save her life. Hence the "desperation" in her voice.
[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.
The grandmother was curled up under the dashboard, hoping she was injured so that Bailey's wrath would not come down on her all at once. (65)
The grandmother has indirectly caused the accident in three different ways. In the first case, she proposes they go to the plantation, and even lies to win over the kids. Then she leads everyone down the wrong trail. Finally, she startles the camouflaged cat into jumping on Bailey while he's driving. She could feel guilty about a lot. But instead of facing the anger of her son, she hopes that she's gotten injured so she can have his sympathy. To that end, she later makes the suspect claim that she's injured an organ.
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.