although it doesn't happen to my car at every stop. sometimes the idle will drop down smoothly to 800. other times after i push the clutch in the idle will just plummet and drop below 500 and then either come back up to 800 or idle at 500-600 and shake like you said. so im interested to see if you find a solution.
also check to see if pressing the brake brings your idle down. i had that problem before so my car used to shake almost every time from the idle being too low at stops. and that ended up being due to a cracked brake booster hose.