Steering wheel shaking at high speeds pulls to the right sometime

Warped brake rotor usually cause high vibration at high speeds. But you can also feel it at lower speeds. But bad ball joints and tie rod end will cause vibration at high speeds. Ball joints will pop at pot holes, sometimes. Tie rods can be felt in the steering wheel at a stop. Move the wheel slightly to the left and right, you can feel/hear a tap as you turn it.

check wheel nuts for tension ( possible theft attempt on the wheels)
check wheel bearing condition and adjustment
check steering rod ball joints and suspension mounts
have a wheel alignment done for possible alter to the settings from the road.

Have a front end suspension check done to eliminate any worm ball joints -shockies- worn suspension rubbers-- steering problems. If ok have a wheel alignment done and have the rear end aligned first as it affects the front alignment. The violent wobble is castor wobble and indicates negative castor possible from sagging suspension springs. The camber is out at that results in the car following every dip in the road. The camber has to work in conjunction with the toe-in measurement and if the 2 are not correct then you will have problems.

Have a wheel alignment and suspension check . Check brake pads thickness and disc rotor condition. Shaking at speed indicates wheel alignment and worn tie rod ball joints and/ suspension badly worn

Check your front suspension(ball joints, tie rod ends, also check the boots for wear and make sure they are full of grease) for tightness. If the vehicle pulls either way or grinds when you turn or brake, it may also be your wheel bearings.

Check tire inflation, brakes, and alignment, in that order.

A steering vibration at high speeds is usually a result of front tire imbalance. A loose or worn front suspension or steering component can sometimes cause a vibration as well. You should check over all the joints (ie: tie rods, ball joints, track bar etc) and if that checks out have the front tires balanced.

Have you checked tire balance and wear?
High speed shake is most commonly tires

ball joint
control arm
shocks
brake rotor
and all your suspension parts have them check by your mechanic

You might take a close look at the ball joints on the front suspension/steering arms. I've had the same problem on another vehicle. Also you should check the front wheel bearings for loose play.