The conflict at the beginning of the story is that the grandmother does not want to go to Florida.
At the beginning of the story, the grandmother is trying to convince her son that they should not leave because there is a dangerous criminal called The Misfit on the loose. She really just does not want to go to Florida.
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. Bailey was the son she lived with, her only boy.
The grandmother tells her son that she wants to go to Tennessee, but he does not listen. They go to Florida anyway, and she brings her cat. However, they go on the back roads.
She said she thought it was going to be a good day for driving, neither too hot nor too cold, and she cautioned Bailey that the speed limit was fifty-five miles an hour and that the patrolmen hid themselves behind billboards and small clumps of trees and sped out after you before you had a chance to slow down. She pointed out interesting details of the scenery…
Of course, as they are in the country, driving slow, the grandmother’s cat escapes and they crash the car. This gives them the opportunity for a new conflict. They run into a group of criminals, including the escaped convict The Misfit that the grandmother warned them about.
Family vacations are never easy. Ironically, the grandmother used The Misfit as a reason not to go on the trip, but she was the reason that they ran into The Misfit and his crew in the first place! The family is killed because of her actions, while the grandmother and the Misfit have an interesting chat about faith, after which she reveals that she knows him because she is his mother—and then he murders her. This story shows that you never can tell about people. The conversation, and the revelation, clearly have an effect on him. There is more to the story that we do not know.