Spinosad is a very nice insecticide, as is permethrin, and both are approved for use on poultry in the USA, with no egg withdrawal period.
Permethrin is very inexpensive, easy to find at any farm store, and works very well.
Here we won't use the spinosad until such time as our local mites or lice develop immunity to the permethrin.
And local wild birds bring the mites or lice to your chickens and the coop, because those rotten house wrens, at least come for the feed whenever the coop door is open. Keeping the chickens inside 24/7, with no outside contact, is the only way to totally avoid these parasites.
Your neighbor's pigeons may or may not have mites or lice too.
Mary