That's really slow all around.
Are you wired or wireless at one end or both ends? If wireless try wired [if possible] and see if the issue still exists.
Are you pulling the movie up directly from the A-TV or trying to AirPlay it from the computer.. I always skip the AirPlay and pull it up directly from the A-TV via my server.
I've never had anything nearly of what you're describing, but when it seems to start slowing down for me a re-boot of modem and router speeds it right back up.