Dramatic irony is used in Shirley Jackson's "Charles" as the mother/narrator never suspects that the poorly-behaved boy about whom her son speaks is, in actuality, her own child, Laurie while readers soon realize the truth.
In the exposition there are suggestions that Laurie is not too well-behaved because as she watches him go off to kindergarten escorted by the older girl who lives next door, the doting mother sentimentally feels that an "era" of her life has ended,
...my sweet-voiced nursery-school tot replaced by a longtrousered, swaggering character who forgot to stop at the corner and wave good-bye to me
Notably, she does not call to him and scold him for his behavior. Also, whenever Laurie describes what Charles has done, neither of the parents question Laurie about his own behavior at school. Instead, they become absorbed in the narrative about Charles. Thus, the reader begins to suspect that the narrative has a meaning beyond what is on the surface [dramatic irony], while the parents in the narrative do not recognize the reality. Part of the reason for their misunderstanding is indicated from an early passage in which Jackson hints at this naïveté of the parents when Charles returns the first day:
At lunch he spoke insolently to his father, spilled his baby sister’s milk, and remarked that his teacher said we were not to take the name of the Lord in vain.
Obviously, then, the parents themselves are not too well-behaved.
Finally, the "ironic punch" is delivered when the mother attends the PTA meeting, eager to see who the badly-behaved boy named Charles is. When she speaks with the teacher, Laurie's teacher mentions that he was rather difficult at first, but he has adjusted with only some minor "lapses." Laurie's mother states her belief that her son's lapses must be due to Charles. Confused, the teacher repeats the name questioningly, "Charles?"
“Yes,” I [the mother] said, laughing, “you must have your hands full in that kindergarten, with Charles.
“Charles?” she said. “We don’t have any Charles in the kindergarten.”