All this trouble over an easily prevented problem.
Some basic facts that will never change.
Rats and mice will live within a few dozen feet of their food source.
Natural environments will not be able to support more than one mouse or rat per a few thousand square yards.
Which is why most wild critters are territorial, to protect their turf and their food supply.
Any rat or mouse that has to travel to find food will quickly become dinner for a predator.
You are dealing with rats or mice because you are not practicing feed sanitation. Get a proper treadle feeder, put the bulk feed in metal trash cans or barrels.
Clean up the area so the rodents don't have cover as they are traveling.
Problem solved in the chicken coop, 100% of the time. No poisons, no shooting, no killing, no continual problem and expense. Less disease and pests like lice and mites coming in contract with your flock.