Bottom line - poorly written article by AP and family trying to pull a fast one.
They were banking that Delta would succumb to their demand based on recent airline events.
If 18 year old went on an earlier flight then it's an empty sear regardless if they bought another ticket for the earlier flight.  They needed to cancel the reservation and get a credit for use on a future flight, with an added change fee of course, and buy another ticket for the toddler if they want the child to have a seat.