2001 Hyundai Accent Vibration at low speeds

An alignment problem won't cause this but what did the person doing the inspections have to say?

The first step is to run the car in gear on a hoist so you can watch the wheels and tires. To be shaking as badly as you described, the cause should be pretty easy to see. Common causes are a broken tire belt, bent wheel, bent hub, and to a lesser extent, a warped brake rotor.

If this shaking is felt in the steering wheel and occurs more when you're accelerating and turning, a real good but elusive suspect is an inner cv joint housing. Wear spots occur that impede the joint's ability to change length and angle as the shaft rotates. That causes it to push and pull on the spindle which tugs on the steering linkage and steering wheel.