VIBRATION WHEN TRYING TO BUILD UP SPEED

First suspect would be a worn front inner cv joint housing. The rollers bind when running back and forth through the worn spots. This is worse when under load as in accelerating. Once you start cruising, the lower torque allows the rollers to roll freely and stop binding. When the binding occurs, the joint can't change length freely as it needs to do three times per wheel revolution. Instead, the half shaft pushes and pulls on the spindle and steering linkage which tugs on the steering wheel.