I agree with everything you said here and I also agree that this couple seems VERY entitled.
BUT...
Anyone who says this is a big mess either does not have kids or does not remember when your kids were this age. The kids did not get into a popcorn fight - they just dropped some popcorn. It's really not that big of a deal. You also cannot just demand that the kids pick it up because they are on a moving airplane and presumably are seat belted for the duration. What are you going to do? Go into demanding parent mode to teach them a life lesson just when all the other passengers are dislodging suitcases from the bins above their heads? That's why I side with the parents - but just by a hair.
Going back to the parents, yes, Mom should have done a little clean-up, maybe even been apologetic, but I am sure she did not and was not. That's why I believe they are acting entitled and probably what pushed the button of the FA that made this an issue in the first place. If that was the case, I would side with the FA, but, being in the service industry, it's really not her position to "parent" the Mom either. That would just cause problems, like, you know, pictures being taken, social media being posted, airline customer care being involved, all that rot. Who needs it?
Personally when flying with my kids, especially when they were younger, we always sat in the back of the plane. That way we were not in the way of the flight crew or the other passengers no matter what might transpire during the flight.