Kari, in my experience, a broody hen who's at the 'sitting tight' stage (think a suspiciously glaring, immoveable, growling puffball) can be moved anywhere there's some eggs or chicks.
I'd recommend separating her and her babies for at least a few weeks: the chicks probably wont be able to reach the nesting box and chickens other than the mother can be really brutal to chicks.
If having more chicks and less eggs isn't to be desired, it's often possible to de-cluck chickens
if you get them early on by putting them in a
well-lit, small, exposed area for a few days with plenty of food and water.
Over here, the outside part of working-dog runs is a popular option.
It's vital that there's nowhere dark and private: they have to be really put off the whole idea
I must have known individual chickens that didn't go broody, but considering a traditional breed like the barred rock hasn't had all the 'normal' bred out of it, I think it's probably as you suggest, and the breeder's conditions were not good for broodies.