Most tournaments I've been to, the kids and parents are pretty well behaved. I think it partly depends on the TD. Some make sure the parents understand they're not allowed in the playing hall while games are going on.
Young kids are annoying though, like you said they fidget and make noise, etc. Luckily there aren't many I have to play against. And when they're teens, at least they're able to sit in their chair and be quiet.
Two incidents recently. Situation -- OTB tournament in which kids and adults were mixed in lower sections. First, when playing, an adult swore (mildly) after hanging a piece. The kid left the board and shortly returned. Then the TD appeared and watched the game for nearly 10 minutes. Afterwards, the adult player was informed that the kid had gone to his parent and reported the swear word. The parent complained to the TD that the adult was using "bad" language in the presence of a child and that children should not be exposed to such behavior. Second, a very, very young girl was playing. She could not record her moves nor fill in her score sheet -- so her mother appeared and was doing it for her. The adult player opined that if a player was unable to write her own name, she shouldn't be playing with adults. The mother reported him to the TD as being offensive to her daughter. In both cases, the TD stated that kids should be allowed different behavior because they are kids.
I was not the adult in either case.
However, I have experienced kids who drum on the table, chat with other kids who are wandering around, kick the table repeatedly, hum, and so on. None of it is malicious, but it is constantly distracting. I have experienced parents who wander in and observe their kid playing and who get their kid settled in before a match (checking on water, checking on the board setup and the scoresheet setup, giving pep talks) -- in spite of rules that say parents are not allowed in the playing area
So, why are kids playing with adults while they are still acting like kids? Why are parents tolerated to closely monitor their kids before and during play? Scholastic sections and contests are available withing their rating range, but they seem to need to get in with the adults.