I was inexperienced with this until a few weeks ago, but my broody threw every curve ball she had at me.
Yes, you can give her any fertile eggs to sit on. Depending on personality you might not even need to sneak the eggs under her. I tucked my broody hen under my arm while she watched me fill her box with eggs and she was perfectly content to go right back to sitting but there is the occasional broody that won't accept new eggs.
There are benefits to giving her a private space, some broodys don't like giving up their original box (like mine) so try moving her in the middle of the night to her new space while she's still on fake eggs to see if she settles back into her new digs without worrying about her abandoning real eggs. I allowed my girl to go back to the box she wanted and in the end this was a poor decision on my part because even though I was free ranging the other girls daily so they would leave her alone, we had a hawk patrolling the yard so I left them in their run for a couple days and that was enough time for them to harrass her off the eggs, lay their own with hers, and she ended up abandoning all of them on day 19 of incubation. There are plenty of people that have had successful hatches without separating them though, just mark the fertile eggs with a crayon so you know which ones they are because other chickens will keep laying their eggs in the same box with her, lol.
When I feel brave enough to allow a broody to sit on eggs again I'll likely keep an incubator on standby the entire time just in case I need to step in. Don't let my experience discourage you though! I found it to be a difficult learning experience but once you have a good broody momma you can be sure she'll always be good at it! I was told when a broody doesn't do well once, don't let her do it again. Good luck! I hope you have some happy healthy peeps following their momma around soon!
