2000 Chevy Cavalier Stuck sparck plug

Spark plugs screw into the heads' combustion chamber. The combustion chamber is the most important and pressurized area of any internal combustion engine. Your Head is made of aluminium--a very soft material. If the spark plugs are installed too tight they will sieze into the head or they will strip out the threads. I do not think your mechanic is telling you the truth when he or she tells you that they can only move the spark plug a little bit. If the spark plug moves it will come out. Nevertheless spray some penitrating oil on the threads of the plug and screw it out. If it is stripped you can install a thread repair kit into the stripped plug hole.
A mechanic that cannot remove a spark plug should not be in business. Change your mechanic!