How do you separate incubating broodies without building another coop?
My problem is my chicken Olive likes to put all the eggs under her before she lays and the other day she even broke an egg because they were fighting over it!
A good reason to isolate her. We all have different experiences and different things work for different people. I don't know what your facilities look like so I don't know what your options are. It would be nice if your coop were big enough to build a pen in it since it should be predator proof inside so you only need something to keep that chicken in and the others out but not everyone has that ability.
Don't think in terms of a coop, you just need a shelter. No roosts and not really that much room. You do need weather and predator protection. You just need enough room for one nest, food, and water. By instinct a broody hen should not poop in her nest but she doesn't have that same instinct in regards to her food or water. So give her a little room to go poop but give yourself access so you can clean when you need to, let alone give her more food and water. Plan on locking her in that pen and other hens out until the chicks hatch. To me you lose the benefits of isolating her if you don't isolate her. It is easier on you too, less work.
One danger in isolating her is that she will break from being broody when you move her. Some hens are easy to move, some not. I find that it works best if the new nest is fairly dark. I've been known to lock a hen in the very dark nest for the day after I move her, letting her out at the very end of the day if she wants to come out. Many hens don't come out until the next morning.
Where to build this shelter? My preference is inside the coop if you can. Some people can build a pen around the current nest so they don't have to move her. Most people cannot do that. My next preference is in the run if you can. That way the hen can raise the chicks with the flock during the day and should return to that shelter at night so you can lock them away safe from predators. Some people use an outbuilding, say a shed or garage. Some people even bring them inside their home, maybe a basement but maybe a utility room, spare bathroom or bedroom, wherever. It's not something I'd do but some people do.
You do not want this nest or shelter to become an oven in the sun. Think about shade and ventilation.
Good luck!