So my question is can I put all 3 girls together in a coop?
Maybe
Will they know which eggs are theirs?
Not really. They might each stay on one nest, but they might not.
Will they bother each other?
Maybe. Two or three might share one nest (chance of broken eggs as they all shuffle around), they might trade nests back and forth, one might try to chase the others away, or they might each sit on their own nest. There's no good way to predict what they might do.
You could let one hen sit, and break the broodiness of the others.
You could put them all in that coop, give each one some fake eggs, and watch what happens.
But even if they seem fine with eggs, they could have trouble after the chicks hatch. One hen might attack the chicks of another hen. Or one hen might try to steal the chicks of another hen. And while it's not a big problem if chicks get mothered by a different hen, it CAN be a problem if there are too many to fit under her at bedtime!
I have seen cases where hens shared a nest and raised chicks together, and everything was fine-- but for every one case that works, there seem to be plenty of other ones that do not work.
We want to build them a small separate coop away from the rest of the flock so the other hens don't keep laying eggs on top of them and mixing new eggs with eggs that have already been brooded for a few days.
That's a good idea, but you might want to make it with removable dividers. That way you can separate hens if needed, or use it as one larger space at other times.