Steering is bad

it is stablize bar or steering box Heavy Duty Jeep Steering Stabilizer

Check your lower and upper control arm ball joints as well as the tie rod ends. Also make sure your wheel lugs are tight. Also make sure front hubs are in the free position when operating on the street. If the Jeep has a straight axel, check the king pin bushings at the steering knuckles.

Replace the swing arm.

Could be a bad tire or is just out of alignment.Alignment is something that has to be maintained from time to time.I would take the car to a good tire shop and they should be able to help you.

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.

if it shakes over 50 miles per hour, it could be your front tires need balancing. and check your ball joints while you are at it. or king pins if it has that. (they are different from ball joints but serve the same purpose.)

NO THEY DID NOT COME WITH A DAMPER, IF U ARE ALL OVER THE ROAD YOU MOST LIKELY HAVE WORN PARTS OR FRONT END ALIGN ISSUES OR TIRE ISSUES, HAS ALL THIS BEEN CHECKED? LET ME KNOW.

Could be a number of things from ball joints to your pitman arm(arm that steers the tires). It dont sound like tire are way out of balance because yu said it only starts when you hit a bump. If it was me, Id crawl under the front end and start shaking different parts until I figured out what was loose. if its shaking that bad you should definitly be able to tell when you shake it.

I have driven one that does this! When it does it, you can barely keep it on the road! Jeep calls this DEATH WOBBLE. Google it to learn more. I fixed the one I worked on by replacing the front tires. The tires I took off didn't look like they had a darn thing wrong with them. But when I put the Full size spare on the Left Front, the problem was gone. We also replace the steering stabilizer, shocks and tie rods on it too, but did nothing to the problem. After the customer replaced the tires, the problem has not came back. This was three years ago.

May check your ball joints and tie rods. Also could be your shocks.
Does it seem like its more shaking on the left or right? or even?