By the way, I was thinking about turning a goat onto its back today to cut it's feet. And whilst I think it's fine to do that with a goat that isn't in milk, I wouldn't do it to a dairy goat in milk. Dairy goats have big udders, and there is no gaurantee they wouldn't bruise it on the way down, or kick it themselves. As even a bruise can cause mastitis, I would avoid it. No harm doing it on other goats though.
Beth