You can't "make" a hen go broody. The broodiness has been bred out of many strains, and they rarely brood. Others still trip right over into broodiness at the mere sight of an egg, or even without it. Some of mine see a darkened nest site, and boom, there they are, brooding straw.
Cochins are usually good moms, but yours evidently hasn't heard the hormonal call. Some say that feeding cracked corn raises body temp, and can help push a hen over into broodiness. Keeping her locked up won't do anything but annoy her.
Golf balls make good fake eggs. You could let her rejoin the other birds, start feeding some cracked corn, and keep a handful of golf balls, (or ping pong balls, or wooden eggs, they're not picky, hens have been known to brood light bulbs and peach pits) and if she goes broody, she'll pick a nest and camp out in it, and squawk and growl at you if you bother her on the nest.
She'll stay on it even at night, instead roosting normally.
At that point, you can give her a clutch of fertile eggs, (they don't have to be just her eggs) all at the same time, marked and dated, so you'll be able to easily identify any new eggs that other hens may lay in her nest, because you need to take those out everyday, and only leave the original marked eggs.
Then, with luck, 21 days later she'll have a clutch of chicks.
This may seem like a dumb question, but you do have a roo, don't you?