The Southern setting is very important to the story for a few reasons. First off, the "good man" the grandmother keeps talking about seems to be the sort of person from the past, and not necessarily what we would consider a good man. There are a few suggestions in the story that the grandmother grew up on a plantation and came from a family of slave owners. This creates her subtle racism throughout the story, such as with the boy they pass on the side of the road and the watermelon story she tells. Her idea of a good man is a bit off compared to what the everyday person today thinks of as good.
As for how her ties to the past are keys to the action, first you have to realize how manipulative she is. She wants to visit a plantation she remembers, but knows her son won't go. So she manipulates the children into helping her by mentioning the secret room full of valuables. Once she has the kids on her side, they complain until her son finally agrees. They drive on this dirt road for a while, when the grandmother realizes she has it all wrong; the plantation she remembers is nowhere near there. Rather than admit she made a mistake, she lets him keep going, leading them to the crash and then the run-in with The Misfit.
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