Should I move broody hen?

One of my Buff Orpingtons decided to go broody on me. We added a rooster to our flock this year and he's been doing his thing, so I decided to let her go ahead and sit. I popped all the eggs that were laid yesterday under her (11 of them) and she seems to be happily sitting on them.

My question is-- should I leave her in the main coop or move her to the barn into a stall all by herself? I have 16 other hens plus the rooster, and 4 nesting boxes in the coop now. The nest box she decided to sit in is one of the favorite nesting boxes, so I'm a little concerned about the other ladies trying to shove her out. It's also elevated about 2 feet off the ground on a platform, with no ramp down -- the full grown hens hop on and off no problem, but I am a little concerned about the chicks getting down when/if they hatch.

I have a totally empty 10x10 stall in my barn right now that has fresh woodchips down -- would it be better to move her there so she isn't bothered? And if so, how soon would you advise moving her and the chicks back after they hatch? I'd really love to have the opportunity to see mama raise them "as nature intended" and let her take them outside to free range, etc. rather than being shut up in the barn.

If you have predator proof secondary quarters, by all means, move her.
However, you'll need to build a nest similar to the one she is on or she may not take to it. The same type of nesting material is most important.
I moved a hen that had been on an excelsior nest and moved her and eggs to a plastic nest pad. She refused to sit. I swapped it out with excelsior and she moved right in.
Sometimes it's best to move her at night. Move the eggs first and sit her on them.
Brooding in the main coop works. The probable is that you'll have to mark all the eggs under her so you can remove volunteers daily. Also, as you've learned, they like to brood in everyone's favorite nest.
IMHO, things just go more smoothly when they have a broody apartment.

When chicks hatch, you can feed them and the hen starter feed and not worry about feed types.
However, you want to move her and the chicks back with the flock before she weans them so she'll protect them from the other birds. Otherwise, you'll have to keep them separate till the chicks are old enough to protect themselves.

Thanks for the advice!

Her nest box is actually just a Rubbermaid tote-bin thing with a hole cut in it, so I could pick up the entire box and move it as-is, to the barn. I can always put another one in the main coop to replace it temporarily.

Perfecto.