I have a 2001 Monte Carlo. When I am accelerating, especially up hills, it shakes, sometimes really badly. If I let off the gas, the shaking totally stops. The shaking is the worst between about 15mph to about 45mph. When I get up to highway speed, it is greatly reduced. It shifts fine without any hard jolts or anything. I know my right front wheel hub needs replaced since it is causing an issue with my traction system. Could this also be the cause of this shaking?

 

From experience, your issue is probably coming from a bad CV joint (axle). I had the same symptoms, shaking while on the gas, and perfect while coasting. Replaced both axles and the shake was gone.

Fixing the hub wouldn't hurt, but I don't think that would cause the same issues that a bad axle would. And, while everything is off, it would be an excellent time to pop the axle (half-shaft) out and replace it. Have you inspected the front at all? Sometimes you can see that a boot on one or both of the axles may have ripped or failed in some way. It was obvious for me because the condition of the boots were poor at best, and grease from inside the boot had coated the area.

Since I had the extra money at the time, I went ahead and replaced both hubs and axles. If money's tight for you, you could probably have a local shop take a look at it and diagnose which side for sure needs replaced, and go from there. Best of luck getting your Monte operating smoothly again

 

One way to kinda test the CV that I know of is to roll down your windows and drive slow past a solid wall and listen for clicking and grinding sounds. Being next to a wall will bounce the sounds back to you hence the suggestion.

But because of your situation you may hear some noise come from the already existing condition not sure. You would be a better judge since you drive it and are familiar with the sounds it makes.

But as suggested inspect the boots. That is almost always where problems with a CV begin. I did have a bad CV on my 3rd gen duster though without a bad boot. The CV just caved under the abuse. I was pretty hard on that car but who could resist the urge in one of those lol.