Oh dear oh dear
If the CAA have put their instructions in writing send them to the AME. Otherwise inform him. If he still refuses you will need to inform the CAA the AME is refusing to carry out his duties. you could cc the CMO at the CAA. you can even escalate to the GMC but this is just daft. The CAA need to be told the AME is not playing ball and send him clear instructions to comply.
noflynomore is correct - this has to be resolved via the AME and CAA. You cant go second guessing the CAA