Steering wheel shakes

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.

1) Take car to non dealer shops willing to give FREE opinion

2) Not likely you have a shock in Driver Front wheel, more likely a strut. Not likely strut needs to be replaced, but strut has a STRUT MOUNT (3 bolts of which can be seen when opening your hood) below this it is connected to STRUT BEARING which below it connects to UPPER SEAT OF STRUT or SPRING INSULATOR, that if loose will rattle. Usually, shops will not tighten, because to tighten is same labor as replace the parts. (Since you already dropped $1000 on ToyotaDealer, ask them to tighten FOR FREE since rattle is still there.)

3) There is a part called a "link," connects strut to stablizer bar, that if bushings are bad will rattle.
4) If stabilizer bar bushing(s) bad, will rattle early on but eventually clunking
5) Bad ball joint or tie rod can rattle as well

Never permit any shop to do expensive work on your car w/o first getting a second opinion somewhere else first. Do not tell second shop that you are there for a second opinion.

Shaking steering wheel at highway speed, no braking
1) Bad tire in front, bad tires in front, verify inflation of tires
2) Wheel alignment may be out
3) Front suspension parts (mentioned several above)

Highway speed to suddenly braking shakes steering wheel
1) Front brake rotors need to be inspected for warping
2) Test calipers on empty road at 40 mph, going straight on very LEVEL ROAD, hit brake pedal SOMEWHAT hard while barely touching steering wheel. If car jerks to one side, instead of braking straight on, you may have a caliper, ABS, or brake fluid pressure regulator off.
3) If brake rotors are warped, may as well replace front brake pads at same moment. Use ceramic.
4) When you drive on VERY LEVEL road on highway, steering wheel must be centered, let go lightly of steering wheel. Did car stay in middle of lane? No? Get a 4-wheel alignment.

Well, short of hurting your feelings.

When you brake you hear a strange noise. The sounds brakes may make, should be something you are familair with.

When doing 45 mph plus, the car starts to shake. Now tell me, youv'e not experienced this many times in your life!

Turning left or right could be a worn steering rack,mostly because you never change power steering fluid,or upper strut bearings or any other suspension parts starting to wear. Or, it's just you noticing different sounds, than when it was new.

When you turn the wheel too far to either side,you hear the power steering pump squealing and telling you to stop. Another bad practice.

Now I would conclude, that you need to strip all four brakes off the vehicle and completely go through some sort of brake repair or service. I hope you already figured that.

does it make any difference turning left or right? like if you are on the highway and changing lanes? does it change pitch? any difference braking or not?? the fr brakes and the wheel bearings need to be checked but you really need to be more specific to narrow the problem down.

try to replace the wheel bearings.

Front shocks are week

I believe you need your disk brake rotors turned to be true again or have them replaced. Whe you use your brakes a lot and kit puddles of cold water then it will warp the rotors which will cause the violent shaking. You may not feel it in the brake pedal even if it is warped rotors. If you don't think you have warped rotors then you should be very careful driving it because it will probably be in the steering sector arm or the idler arm on the steering shaft.
Dale

Have the brake discs checked, as they may need to be machined or replaced.Also have them check the idler arm and tie rod ends.

Sounds like your brake rotors.You dont have to feel it in the pedal to get a shake in the wheel.