I think the Delaware would be a great choice around children, plus all the other requirements you have. Production Reds, I believe, have been bred towards egg laying and away from brooding chicks. Doesn't mean it won't happen, just not very likely. Orpingtons are also very docile and make...
Buckeye's are great for all that too, except maybe hatching their own chicks. I don't have any buckeye's, but I've been reading up on them. I agree that Delaware's would also be a good choice.
ETA: I'm also wanting a good dual purpose breed, so I've been researching. But I don't need cold...