We have similar set up - coops attached to a run that's a cube 8x8x8, like a bird cage, all wrapped up and with tarp as inner roof. And the entire set up is inside an extended fenced in area 30x50 (chicken wire + deer net).
Our "cube-cage" run is covered with marine vinyl for the winter, leaving top 1 to 2 ft top section open for ventilation, also surrounded with hardware cloth apron - complete predator proof. The cube is attached to the coops that chickens can go in and out freely any time. The cube has a full human size door that leads to the extended run, which we close up every night.
The extended run is covered with aviary nettings (we have hawks), and hardware cloth apron (we have foxes) all around. It is as much as we can do for predator-proof, but it is probably not enough for determined racoons.
Chickens can go freely during the day wherever they want in the entire fenced in area no matter what the weather is like, but at night, they are locked in the cube/coop (the coop door is open 24 hr since the entire cube/coop complex is predator proof. Unless it is really rainy or stormy, or with hawks around, they like to be out in the extended area. They have good innate judgement for weather and hawks, but not foxes!! We've seen our chickens do nothing when the fox was outside the fence staring at them, or walked by the area!!!