My steering wheel starts shaking between 50 and 60 mph.

possible a wheel alignment possibly from the rear wheels and loose/worn suspension rubbers

go to a mekanic and have t look at the the wheel bearings

REbalance tires.

I doubt these problems have anything to do with each other.The shaking steering wheel could be an out of balance or bad tire(torn belt),a bent wheel,or improperly tightened lug nuts(not torqued evenly).The check engine light will require a code scanner to see what the code is.(if you work on your own cars,you might want to buy at least an entry-level code reader/clearer,some are under 50 bucks).

Start by checking the tie rod ends on both sides on the front wheels..With the truck jacked up and jack stands underneath the frame both left and right wheels should be suspended in mid air..The are two tie rod ends on each side of the vehicle, a inside and outside tie rod..Check for any excessive place on each one...
Also ckeck the balance on all four tire's... Inspect the wheels for any stress cracks that would cause them to not to balance correctly and make your vehicle shake...
Check the transmission mounts on the cross member,make sure the mount is secure to the Trans and cross member mount..Also check both u-joints on the drive shaft and any hanger bearings that may be underneath there..If it's a 4 wheel drive check both drive shaft's...Anyone of these option's could show those
symtom's you mentioned...Good luck and let me know how it works out..

The shaking may be a separated tire.

If the check engine light is on there will be a code. Have the computer scanned for trouble codes to see why the light is on.

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A shop didnt find anything? You have a suspension problem Lets start at the tires is there any mud or crude that affect the balance of your tire? What about wheel bearing is there side to side movement even with the rear,How about the upper ball joint and lower ball joint . a warp drive axle can cause this . If you are certain of there inspection with the suspension the problem is the torque convertor. If that stays lock up whoa you will be shaking like big time

I have this same car with exactly the same problem. Begins shaking at 40mph and stops shaking as soon as you let off the gas, but then begins again as soon as you press on the gas and smooths out as you get over 50. And the shaking is not felt through the steering wheel. Solution: Replace the transmission mounts. There are two of them, one on each side mounted on the frame right next to the shock strut. There is also a front and rear engine mount, but I replaced the two as described and shaking is gone.

Front shocks are week

try the simple solution first put your front tires on back and back tires on front. check your air pressure then take it for a drive and see if any thing has changed. if so you probably have a badly worn tire. if no change have someone move the steering wheel back and forth wyle you are under the fornt of the car (dont forget to chalk the wheels) and see if any of your steering components are loose/moving. if nothing is loose and your tires are good try to bounce the front end. if you can really get the front of the car going up and down pretty easy you havce bad struts/shocks.