To answer your question, yes, I think you should be concerned about the possibility a racoon will take a chicken during the day. When I lived in a more suburban area I saw racoons out during the day fairly regularly. Now that I'm in a rural area, I never see them during the day - but it doesn't mean they're not there, along with bobcats, skunks, etc. I think that the closer these animals are to civilzation, the more accustomed they are to people and they stick less to their natural nocturnal instincts. Heck - I've seen the 'dawn/dusk' predators out hunting at 10am. Not only that, but you've got the free ranging chickens as a draw and children in the yard - coons are vicious and nasty and I'd be concerned about the possibility of one of them attacking you or a child if it was trying to get to the chickens.
Do you have animal control that you can call?