Keeping other hens from accessing nests because of 1 broody is more likely to cause the other hens to start laying elsewhere, thus increasing the amount of problems you're dealing with.
They'll break more easily/consistently if they're kept caged around the clock until signs of broodiness diminish. I only recommend removing them from the cage/crate at night if the cage is located somewhere that's not predator safe or safe from the elements (i.e. wind/rain, "cooler night temperatures" is not a reason to remove them from a cage).