Try an experiment. In the comfort of your home, get out your favorite pistol and pretend you are at the range. Hold it up, sight down the sights, and pretend to shoot. Do this for the duration you would normally do at the range.
If you don't get the shakes at home, then that would leave me to believe the problem is either fatigue, dehydration, or recoil/sound related. I.E, something that is introduced at the range itself.
If you do get the shakes at home, that would lead me to believe you have a neuro/muscullar problem (either lack of strength or a medical issue).