Each of us do this differently. I would want my chicks in the big girls coop. I would keep the big girls in the little coop for a few days. Are the young birds roosting in the big girls coop? That is what you want.
Then I would open let the big girls out into the run with the chicks about thirty minutes before dark, locking the little coop from all. I would expect them to all go to sleep in the big coop and integration to be over. No need to drag it out forever.
Some people will leave both options open and let the birds make their own choices. Then when most are in the bigger coop, shut off the other.
Do not have them pass in the night, that is way too much fiddling around for no reason at all.
With your patience I would expect the meeting to be almost anticlimactic. If it is not, I would expect a bit of bluster, a charge or two, bluffs in and over.
Mrs k