My son (13) practiced aikido from age 4-8 and absolutely hated it! He was in a kids class and all they did was play games and do some shikko and rolling and tenkan. When I started my dojo, I didn't have enough students to practice with, so I've convinced him to come to class once a week. He is in with the adults, and he's by far my best uke, and really likes it when I toss him around (now he thinks mom is awesome), the more dynamic the better. He's having some trouble with techniques due to being somewhat inattentive, but I definately think that the adult class is the place for him to be. Were he a bit younger, I don't think I'd want him in adults class. As long as you don't do hard joint locks, kids can be tossed around with the best of them.
Now Liane, in answer to your original question; Jun had a very good point, which is talking to the parents to either find out why they are in class, or to have them lay down the law as it were with the kids. Also, Ignacio had a good point about this being a martial art, and that you can infuse discipline into it (actually, I've found that a good kote gaeshi works wonders on my son). And finally, Bronson made an excellent observation about having taken an offender aside and have a talk with him.
Kids do learn differently, and they feed off each other; if one gets silly, then the whole class can degenerate into a silly-fest. I've found that a stricter teacher generally has better control with the kids, and they typically like that teacher better than one who lets them run rough-shod all over the place.
All the best,