Issue with tire after rotation

There are a few things to consider. First, some cars have the alignment set for comfort or handling over tire wear. Radical alignment settings result in tire wear patterns that make noise when they are tipped the other way. A lot of cars call for the rear wheels to be tipped in on top, and the front to be tipped out on top. The car manufacturers call for the tires to be rotated often to even out that wear. This can be as little as every 6,000 miles. At higher mileage intervals, the wear can cause the noise you are hearing. The clue is found by running your hand around the tire to feel the wear patterns. Specifically what you are looking for is each block of rubber will have one edge raised higher than on the other side. You will feel your hand slide relatively easily in one direction, but catch on the sharp raised edges when going the other way.

You did not list the engine size or correct mileage so I cannot make any generalizations based on that. I looked up a representative model, and found your car calls for some pretty extreme alignment settings. No alignment specialist will be comfortable with those specs if he has to warranty his tires based on mileage. The rear wheels in particular are tipped in on top a real lot. The fronts are also tipped in, but not as much. You will find the tires will wear out on the inner edges faster than the rest of the tread.

The shaking steering wheel is usually caused by a broken belt in a tire. That can be hard to notice if it is on the rear, but now that it is moved to the front, you may see that as the steering wheel oscillating back and forth. That can be easier to observe at low speeds or when driving slowly through a parking lot. My recommendation is to return to the shop that did the rotation, and have them inspect the tires. If this was not done at a tire and alignment specialty shop, you may need to go there next for the inspection. Some types of broken tire belts are real hard to identify if you do not know what to look for.

Another cause of steering wheel wobble, especially if you have cast wheels, is a small part of the wheel corroded off near the center, and became stuck between the wheel and hub. That will make the entire wheel wobble. Most of the time that can be seen by eye while running the engine, in gear, on a hoist. For more elusive wheel wobbles, a "dial indicator" is used to measure the amount of "lateral run out" while the wheel is rotating.

Another cause of wobbling steering wheel that we do not see too often any more is failure to properly tighten the lug nuts. Years ago, with big heavy cars, we would zip the lug nuts on with air tools, and never have a problem. Today, with lightweight cars, it is important to use a click-type torque wrench to set the lug nuts to the specified torque. There are four reasons for doing this, but in this case, the important one is so all the nuts are tightened to exactly the same tightness. If they are not, the uneven clamping forces will eventually lead to a warped brake rotor after multiple heating and cooling cycles. That can cause the brake caliper to be shoved back and forth once during each wheel revolution, and while that is often not felt in the brake pedal, the force of moving that mass can tug on the steering linkage, and make it felt in the steering wheel.