Please tell me everything about letting a broody chicken raise day old chicks

We got 6 chickens last year, it was my first time owning chickens. We have a favorite named Lucy, she is so sweet and good natured, she would let my at the time 3 year old daughter hold her and sing to her for hours. She is still our nicest chicken, though she is low on the pecking order.

They have a 9x18 foot run they stay in because we do have a lot of hawks in our neighborhood. I’ve added 12 more feet to the run with a door to separate it and we have 4 chicks ordered to arrive May 9th. Lucy has gone broody, she is our only chicken who has been broody and I would love to let her raise the chicks. I have a small coop separate from the main coop I can put in the new section of their run, I’m thinking about moving her to that area by herself a few days before the chicks will arrive and then sneaking them under her at night. I think because she’s low on the pecking order it will still be hard to integrate them with the other chickens in a few months, but it would have been anyway if we raised them in a brooder in the garage like we did with our chicks last year.

I would love any tips or info about doing this, and if more experienced people think that it’s a good idea.