I would put her in the crate in the garage! That’s what I do with my chickens when they are under the weather - helps them rest and heal and I find it’s easier for me to keep an eye on them to make sure they are eating and drinking. I’d put a little towel or old pillowcase in there for her too, but that’s just me.
After she’s healed up, I recommend putting her in the smaller coop within the run so they can see but not touch each other for a couple of days, following pretty much the same protocol as introducing a new chicken to the flock. It will likely go a lot faster, but you still want to give them all some time to get re-acclimated in case pecking order has changed. When you do let her back out with the others, the best time to do it is when they go up to roost.
Just keep a close eye on her to make sure she’s not being bullied, as chickens tend to pick on the weaker ones for the survival of the flock.
