If the older son went home on an earlier flight because there was extra room on that flight, then the ticket he used was the paid ticket. Therefore, the seat on the flight with the parents and toddler is now open. So, unless the parents bought that open seat, they do not have the right to use it for the toddler. Now, I do not condone how the Delta person spoke to the parents, but I think the parents were just trying to get a freebie. We had that happen once where my daughter flew home on an earlier flight, but our plane was not full either. Her seat was between my wife and me, but no one took it, so when the plane took off, we just used it as "storage" for my wife's jacket and purse once we were in flight. But, we knew that if someone came along to sit there, we did not have a say.