As much as non-poison sounds nice, a good dose of something chemical to kill them all of including a spraying of the coop and roosts is sometimes what it takes. Remember in the meantime they are feasting on your birds- sucking their blood, etc- affecting their health as well. If I were you I would do a single treatment on every bird and on the coop, then repeat again in 5-7 days, and keep your kids from handling the birds in the meantime if that bothers you.
What do you use to spray the coops? I do have a poison powder for them I can and have used. Guess I'll give it a go again.