I believe it has something to do with the local axis for the object & the dummy.
I google searched your problem & came across this thread on gtaforums.com & thus found this video. Hopefully the video helps.
Normally I wouldn't search it up, but it's been at least a year, since I've worked with zModeler.
However, I do know that happened to me once or twice, & if I remember correctly, upon re-importing the car into zModeler, that was shaking, the chassis dummy wasn't in the exact center of the X, Y & Z axis, therefore resulting in the shaking. The farther out it was from center (if I remember correctly), the more "intense" the shaking was.
I apologize ahead of time, if this isn't the solution for you, but like I said it's been at least a year or more since I've worked in zModeler.
Cheers,
KN1IGHT