Sounds like either you have a bent rim(s) or your tie rods are going.
check the motor mounts
Loose Motor Mounts
For serves, volleys, slices, overheads, or certain ways of hitting ground strokes
Wheel balance, Worn steering parts, Worn suspension parts, Tire damage,
Check or replace axles, worn axles are primary source of shaking when accelerating.
you probably have a bad ball joint.
My Dodge Charger doesn't shake...
You need a steering stabalizer and if you have one it may need to be replaced.
Probably the throttle position sensor.
Warped brake rotors........
rear brake drums or rotors are out of round.
it will shake uncontrolabley