The incident happened Aug. 17 when Maribel Martinez said her son, Andy, was supposed to fly from the Dominican Republic to John F. Kennedy International Airport in New York.
"When I went to pick up my son, my son wasn't there," Martinez said at a news conference today. "I was given another boy."
Martinez's attorney, Sanford Rubinstein, added that for more than three hours, Martinez thought her child may have been kidnapped.
It turned out that Martinez's 5-year-old son had been mixed up with another unaccompanied child of the same age, according to JetBlue's manager of corporate communications, Tamara Young.
Andy was supposed to fly to New York, and the other child to Boston, but each "boarded a flight to the incorrect destination," Young told ABC News today in a statement. "Upon learning of the error, our teams in JFK and Boston immediately took steps to assist the children in reaching their correct destinations."
The children "were always under the care and supervision of JetBlue crew members," Young said. However, the airline realized "this situation was distressing for the families."
"In addition to extending our apologies, we refunded the flights and offered the families credit towards future JetBlue flights," Young said. "We are also reviewing the incident with our leadership and Santiago airport team to prevent similar situations from occurring in the future."
Wile Martinez did receive a refund and additional credit, she never got an apology, Rubenstein said at the news conference today.
"Once that investigation is completed, certainly, we will explore a lawsuit," Rubenstein said.