When accelerating car vibrates

A common cause of this is a worn inner CV joint housing. You'll feel the steering wheel tug left and right during acceleration, and it is usually worse when turning to one side, as in when accelerating out of a driveway or parking lot.

I've found that with domestic cars, the worn housing is on the passenger side about eight out of ten times, but there is no way to know for sure. Due to the really low cost today of replacement half shafts, the fastest way to find this is to just replace one shaft, then, if the problem is still there, replace the other one.

The other way to identify the worn housing is to take the inner CV joint apart, then inspect the six highly-polished surfaces the three hardened rollers run on. Once the grease is cleaned out, those surfaces will feel perfectly smooth, but when you shine a light in there, a worn housing will show very slight irregularities in the reflection of that light.

As the half shaft rotates, it has to change length and angle. That is done with the rollers running back and forth on those polished surfaces. They always run in the same area, so that is where the wear takes place. Once the wear is bad enough, the high torque during acceleration puts pressure on the rollers, then they bind when trying to roll out of the worn area. Unable to change length freely, the shaft pushes on the spindle, and that tugs on the steering linkage. During cruising and coasting, there's no pressure on the rollers, so they can run in and out of the worn area freely.

There is always one engine mount that sets the engine's position. If anything is done related to that mount or the engine that moves it sideways a little, that places the rollers in both inner CV joints in a new orientation. That is why this problem often shows up right after other services were done.

This has nothing to do with pulling to one side. That's an alignment or tire issue. You said the entire car vibrates, and only during acceleration. Those are the two elusive symptoms of a worn inner CV joint housing.

Shaking due to an engine misfire will usually also be felt when the car is standing still. Any other shaking besides anything engine-related has to be caused by something that is rotating. That is the half-shafts, brake rotors, tires and wheels. You would feel a broken tire belt or bent wheel at any speed and when coasting, cruising, and accelerating, so we can rule that out. Warped brake rotors can cause a steering wheel oscillation, but more commonly you'll feel a pulsing in the brake pedal. None of those problems occur just when accelerating.

Nothing you have said so far leads me to suspect anything other than an inner CV joint housing. Every comment you've added reinforces my suspicion. I hope I'm not wrong, but if I'm right, you don't want to waste a lot of time and money looking at the wrong things.