Are you allowed to have a shed? Maybe you can disguise it as a shed. If you use wire to cover the top in order to keep all the predators out you should use the 1/4 inch hardware cloth or the 1/2 inch hardware cloth. Anything bigger than that will let predators in.
I hope you have found an answer by now, but you can line the floor with linoleum or use metal baking trays or plastic plant trays to help keep things clean, clean easier. Also, I am now hearing a lot about PDZ as something to use instead of pine shavings or sand.
You are the alpha. Hold the hen down on the ground like a rooster would for a couple minutes in front of the others. She should become docile after that.
Hardware cloth 1/4” or 1/2” is better than poultry netting. It’s stronger and due to the size of the mesh can keep out more predators.
How often do you clean the run out ? The flies are attracted to the rotting smell of the poop and any food scraps.