Actually, the spout is the only thing that should be moving in that situation, seeing that the copper stub out is soldered into the valve. So basically it's like you're unscrewing a cap on the end of the stub out nipple.
After looking at your pic's again, I'm betting that electrolysis has seized the copper stub out into the most likely steel spout threads. Coming out of the wall should've been a brass nipple, not copper pipe with a male adapter soldered onto it, there is zero dielectric break, going from a most likely steel spout to copper pipe. You need a 5" or better yet 6'' long brass nipple between the spout and the valve body as a dielectric break, so that the dissimilar metals don't eat up your copper plumbing system.
Electrolysis will cause all sort of problems, from plaque in the pipes, that will restrict water volume, to pinholes in the copper plumbing system, including water heater, and water softener tanks, it's nasty stuff.
I'm all for trying to fix things myself, but like you, if it's a P.I.T.A, I'm calling in the pro's.
There is good reason why plumbers and skilled tradesmen charge as much as they do, it's because of their training/ knowledge, but the main reason is no sane person wants to work on their own $#!t.
Watch how they fix it, and you'll be good to go if it ever has to be done again.
