I work with children that age every day too and can honestly say there is always one child who acts up at the worst time. Any time my Head Teacher comes into observe a lesson at least one child (and usually the one who you least expect) acts up and suddenly becomes mouth almighty to challenge you. Louis is 4, attended trooping the colour, visited Cardiff, been around family he may not always see but gets indulged by for a long weekend and was probably shattered. Not long after that clip presumably is when Catherine walked him out for a rest before the balcony. It always gets me that people are always so happy W&C raise "such normal children" on one hand but on the other as soon as said "normal children" misbehave in the way any normal child would they are ill prepared for royal life and being appallingly misbehaved. He is 4, he stayed as long as he could - probably on reflection for all a bit too long and then was taken for some downtime before the big balcony appearance. I don't see a problem.
Royal kids in general have more "normal" lives today than they used to in previous times. For starters, they go to normal schools (as opposed to having private tutors behind the Palace walls) and interact wiith other normal kids. And the fact that many of them now have one parent (mother or father) with a middle-class background, I think, makes a difference too. However, they will never be "normal" in the broader sense, especially not the kids who are directly in line, because their lives, as we have seen over this weekend, is somewhat surreal.
It is not really about the palaces, or the privileges (many royals actually live quite stoically), but it is mostly the concept of elevating one family above everyone else in the country in precedence, with soldiers standing in attention when you pass by and people around you acting deferentially or cheering you as we saw in the Jubilee celebrations. As I said before, for people like me, who grew up in republics, that is a concept that is difficult to grasp and, honestly, not being an expert in child psychology, I don't know how a little boy like George for example reacts when he is told he is special and sees that people treat him differently or behave differently around him, or when he realizes that he is destined to fulfill a certain public role and cannot choose a different path in his life. It must be complicated.
Of course, that has nothing to do with Louis's behavior, which, I agree, is a normal reaction a 4-year-old could have under those circumstances.