We have not been group camping in so long, I am not sure we had electricity back then!  Okay, maybe not that long ago, but it was pre-kids and a very different experience.  It was all adults, did rafting and camping - was a blast, but I doubt our advice from that would apply to your group camping trip with kids.  I guess you could modify our "If the beer goes off the raft, you go with it"  to a more kid friendly..."If a kids falls off the raft, perhaps someone should help him" motto?

I have been group camping a few times when I was the only one with a child. We played the regular camp games and he would be on my team so that he could still participate without losing to a bunch of adults (okay, being on my team my have meant he lost...but at least it wasn't his fault). My son actually seemed to get a lot of fun things started just by being a kid. You would be amazed at how much a bunch of childless adults can enjoy trying to catch fireflies at or crayfish under the guise of "helping the boy", lol.

I also took him fishing and to the beach so that the other adults could enjoy some child free time ;)