O'Connor employs repetitive syntax, keeping some sentences quite short, in order to impact tone and mood and even help to develop characterization. Syntax refers to the arrangement of words and phrases in a sentence, and authors can manipulate syntax for a number of reasons. Short, clipped sentences like some of the ones O'Connor uses tend to affect the tone of the story, making it sound somewhat wry and ironic (which is appropriate given the irony of the family's vacation ending in their complete annihilation).
Short sentences can also tend to sound somewhat petulant, also appropriate given that the grandmother also possesses this quality. The first line of the story, "The grandmother didn't want to go to Florida," makes her sound rather childish in this way: there is no explanation or elaboration, just a simple statement of her emotional response. Further, when the grandmother says, "'People did right then,'" to describe the past, the shortness and simplicity of the sentence emphasizes her belief that the past was a simpler time. It's as though this is all there is to say about the past, and that this "fact" alone completely explains all of the grandmother's dissatisfaction with the present.