Peggy Sue just gets in the shower with me, but that doesn't work for my outside goats.
For them I fill a kiddie pool halfway with water then add a couple large stockpots of boiling water to take the chill off. Then I put my children in their swimsuits and put them in the pool to scrub the goats. Everyone gets a quick rinse from the hose when they get out of the pool.
I use cat flea shampoo to get rid of mites and creepy crawlies. It also keeps the children free of external parasites!