Back wheel is shaking does not roll the same *** the others.

did you bleed the air out of the power steering lines -
Getting Air Out of the Power Steering Pump and Lines how to bleed air out of power steering lines Yahoo Video Search Results also if you didnt properly set tie rods or have alignment done your wheels wont be rolling straight and can cause wobble

more detail, please. Does it shake at idle in neutral? If yes, not likely transmission.
Does it shake while sitting still? Only while driving? If while moving, check wheels/tires/brakes.

Very unlikely a bad alternator is going to cause a steering wheel shake even if the alternator is seriously out of balance. In that case a high frequency vibration will run through almost the entire car and the alternator will soon self-destruct.

There are a few reasons why a steering wheel might shake and mostly these relate to the integrity of the front wheels and tyres, the roundness, the radial and axial run-out, the balance and the compatibility with each other and the vehicle. Problems with the wheels and tyres can further be aggravated by steering/suspension wear or misalignment, worn shock absorbers and even binding brakes or warped brake discs.

The rear wheels and tyres and suspension and brakes are also important for a smooth ride and could conceivably cause a steering wheel shake, though a different sort of shake to that caused by the fronts. In this case the vibration is often felt mostly through the seat of the pants and from the seat back.

you may have anything from a bent wheel all the way to suspension issues so do this..take the car to an empty lot big enough you can drive the car around while someone looks at all the wheels looking for abnormalities in each wheel as it rolls slowly around them.even if a tire has a slipped belt, abubble or some out of round issue the car will shake(wiggle side to side whatever) some cars are sensitive to brakes grabbing and causing the same thing..other models have steering dampers(like a shock unit) made into the system that fails, and others have suspension parts and connectors that wear out with uselike ball joints and the like..you may have bad cv joints also(front end driveshafts)so heres what you do..take this list here and do each item at a time to find the reason for the issue and get back to me on what you find...good luck...

check the balance on the tires. if the tires are balanced and roll smoothly check the inner axle joints for excessive play.

Do you have the radio on? Maybe it likes the music... Okay, so enough of that...
The wheel could be bent.
The tire out of round.
The bearing could be bad.
The tie Rod could be out or going out.
The tie rod-end could be bent or worn.
The Ball joint could be allowing it to wander.
Lotsa stuff.
Start with the simple things. Replace the wheel and tire.
If it does not run out okay then move to the tie rod. Lifting the car up and securing it on a jack, shake the wheel in your hands about 3 and 9 o'clock.
Does it feel loose? if so, inner or outer tie rod.
Is the tie rod tube bent? Look at it. Only way is to see it.
Ball joint: Lift the suspension just enough to take the tension off the wheel assy. Shake at twelve o'clock and six o'clock. Does it feel loose?
Any looseness indicates the issue...
roll the wheel on the car. Does it growl? Should like something other than smooth? if so, replace it.
Does that help? Let us know!

get under the vehicle (use ramps) and check all linkages for movement pull push on the anti roll bar links, pull push on steering rack and pinion and linkages, any excessive movement, jack each wheel at a time, using a bar check the lower wishbone joints for movement, get the bar in the gap between the wishbone and lower part of the shock. and pull down, if any movement in ball joint up and down replace. while wheel on vehicle check for movement in bearing you will feel a tiny amount not much but pull and push on wheel with opposite hands on 12 o'clock and 6 o'clock and do the same at 9 and 3. now with both wheels off the ground but with the tyres still on, have some one holed one wheel and push pull on wheels each side there should be even movement between both wheels, if everything is fine with the the steering linkages and this dose not feel or sound right then this could be the problem also to add if the inside and out side of the tyres are wearing then the tyre pressure is wrong and needs adjusting to the right tyre pressure .

Please have the balance of your tires checked. You may also have a ply fault inone of your tires.

Thank you for your interest in FixYa.com

SOUNDS LIKE A LOOSE WHEEL BEARING ...TRY SHAKING WHEEL BY HAND FOR PLAY TO CONFIRM GL

Regarding your window. The window, more than likely, needs a new regulator. 2000 Sonatas are notorious for this problem, I just had my back driver window regular replaced due to not rolling up and falling down when I closed my door! The shop charged me a tad over $100 for the regulator and labor. Not a bad deal considering the cost of the regulator. Good Luck