Gee whiz, sounds dangerous! Has anyone had a look under it to inspect the suspension, brakes, hubs and driveshafts? I would think that with a problem like you describe the offending part would fall under the "gross and obvious" category.

You mention it happening both while at part throttle and in neutral. Does it only happen at a particular speed? Is there any noise along with the jerking/shuddering? I want to guess that you have a failed intermediate shaft carrier bearing or CV joint. That would almost certainly involve a bunch of noise though too.

-Will