Peppermint and spearmint deter rats and mice - but it must be the real stuff. Mix 3 teaspoons essential oil with 1 teaspoon milk to emulsify it, then mix in 1 liter of water and spray in the coop. Repeat every week.
Or grow mint around the coop, so long as the birds don't eat it all up, it will...
I have moved hens of various breeds, together with their eggs, on several occasions. I move the eggs at the same time, so that she's not left wondering where they are while I fetch them. Just put the eggs into a basket. I do it as quickly and quietly as possible, into a ready-prepared nest with...