Not to name names, but a relative of mine recently backed out of her garage for an early AM shift at the hospital and forgot to open the garage. "It's always dark backing up anyhow, I just forgot to put it up". It happens. It's never happend to me, but that's another story. ;-)
Anyhow, it is physically possible to install a mirror on your rig that doesn't vibrate when going down the road. I know, becuase I've done it. Your old mirror didn't vibrate before it was damaged I'll bet, so the replacement shouldn't vibrate either.
Is this a full electric unit? I've never actually taken one of these off before, but the old manual cable units. I assume it's all the same. They're usually held on by a ball-socket union, that allows it to move around when it needs to be adjusted. Usually that's a pressure/elastic type of deal holding it in. Sorry, I can't explain it any better, but I think that's the general idea.
I read you got it done at the dealership, I'd say it's probably under warranty for the work they did, so it should be fixed and they can claim it was defective.