Are you thinking of using Aparasit on the chickens, or just on the coop? It looks pretty strong stuff, and would probably be used on pigeons because people wouldn't be eating their eggs. If you spray your chickens with it, there would need to be a very long egg withdrawal period as it's systemic and will affect the eggs and pass into humans. All the systemic spray-on mite treatments such as Fipronil (Frontline) etc are potentially very harmful to the health of both chickens and humans and should only be used as a very last resort on non-laying birds, if at all. If used in effective quantities on the coop, especially when spraying inside, you need to wear full protective clothing including a chemical mask, and wash everything afterwards including yourself and your hair, as the stuff is carcinogenic.
I think you're right to concentrate on trying to rid the coop of mites - I don't think you've said whether the coop is covered with roofing felt? If so, you need to remove all the felt and the supporting wood underneath, and burn it, as otherwise you will never get rid of the mites and mite eggs that will be tucked up in their hundreds and thousands between the surfaces. Replace it with single-sheet corrugated plastic, which will never need toxic treatments and will also improve ventilation at roof level and give nowhere inaccessible for mites to hide. If you remove the old felt and the wood layer, you will inevitably shake out some of the mites and eggs on to the surrounding ground, so it's best to move the whole coop out of the run if possible, and then stand the legs of the coop in tins of water or D.E. to prevent them crawling back in.
The other problem is dealing with mites that have got between the slats of shiplap coop sides, if you have these, as well as every inaccessible place where two pieces of wood join closely but leave a tiny crack. This is a big problem in wooden coops, and the only solution really is to burn the coop and replace it with a clean one, preferably plastic, which won't have the same problems. Think what you'll save, not only in time but on nasty chemical treatments for a problem that just won't go away!
One more consideration, important if you did change the coop and manage to beat the current mite crop - where are the mites coming from in the first place? Are there any overhanging trees where birds roost, especially pigeons? And do wild birds have any access to the chicken run, or if it's covered in mesh to exclude predators, do they perch on the mesh and shake their feathers? Any of these factors will lead to renewed mite infestation when wild birds preen and mites drop off on to surfaces below. A friend of mine who had never had any redmite left the door open to a clean run and came back to find a pigeon settled on a stool in there. She chased it out and found the stool was covered in redmite. She then used Ficam-W on all the exposed areas and nipped the problem in the bud. I'm sure that excluding wild birds is the main way to prevent infestations. I can only say that, in a roofed run with mesh sides that excludes wild birds, and a plastic coop, I have been keeping chickens for many years and have never encountered any redmite although the run is well shaded by large trees and we have far too many pigeons who live in them!
When you've got the infestation down to a lower level, you might consider using Red Stop in the drinking water. This is a herbal treatment, harmless to chicken and human health, which makes the chickens' blood taste nasty to the mites so they don't feed and thus eventually starve themselves. You use it at a higher concentration for the first week or two and then at a low maintenance dose. Worth a try, especially when you get to the stage of prevention rather than cure.
