A shoe box lid would be perfect although you might think about using the shoe box as they will be throwing it every where and won't be in the lid for long.
The time varies by bird but generally once they are fully feathered Mom kinda starts doing her own thing again.
As far as flock acceptance, depends. They went out of the nest with mom today and one of my older hens challenged mom (over food) but mom went into a crazy mama rage and I had a hen fight on my hands so the other hen is taking a time out in a cage until the babies are a bit older and more sure footed.
Then I watched and saw another young hen pecking at the babies. Mostly curious I think but they weren't moving out of the way so she got another cage until the babies are a little more savvy.
If the broody is a hen that is higher on the pecking order, you have less challenges and issues. I always like to watch them as much as possible the first week to see how the mom and the others are handling it.
...sounds like you have your hands full!
Hopefully I'll be putting my chicks out into their coop this coming weekend. Hubby reckons it'll be finished then. They are certainly getting too big for their brooder.
I've heard to keep them in the coop for a while before letting them out to free range, so they will return to the coop on their own in the evenings. How long should I keep them cooped up?
BTW when I'm watching my chicks I sit with the brooder door open. They come over to me and "groom" my hair!!! Or they come to the open door and sit down and fall asleep close to me. I'm hoping this is normal behaviour. Or at least behaviour that shows they aren't scared of me...