Forgot to say,
what I explained above is similar to what you proposed only the younger pullets would be in the dog cage (although it would be best of you hooked 2 really big dog cages (48") together as their run. One would be too small.
Chickens can be territorial so if you place the new brood in the coop too soon you may start a turf war.
I integrate my flocks of different ages by having an interim run where I keep the new, younger birds locked in for a minimum of 1 week so they can see each other side by side. Then I...