Are you saying you still have the shaking problem and that you can also move the tire about 1"? Then the tire rod end wasn't the problem. Is the shaking dependent on the car speed or engine speed? Check the wheel bearings. There could also be a problem with the drive axle.
Just because a shop put the wheels and tires on a balancing machine doesn't mean the tires are properly balanced. If the shake is car or road speed dependent, it could still be a way out of balance tire. Do you still have the slicers? The wheel should be mounted on the balancing machine with the spring first, then the metal cone, then the wheel, then the plastic cup and the "T" handle to tighten the whole asembly to the backplate. The wheel must be concentricly mounted on the shaft. If you see any rim or tire tread movement while the tire is spinning, there is a chance this didn't happen.