Car wobble

That is the classic symptom of a rear tire with a broken belt. I can describe how to check for that, or the people at any tire and alignment shop can identify a bad tire.

The first suspect is a front tire with a broken belt, especially if the wobble occurs at slow speeds, like when driving through a parking lot. Raise the front end off the ground, then look at the tread area to see if there is a tumor, or raised area on one side of the tread, or the tread squirms in an "s"-curve pattern as the tire rotates. Be careful because broken belts are often accompanied by the wires of the belt sticking out and they can poke your fingers. That can be very painful. It is easier to watch the tire while running the engine, in gear. Only one tire will rotate. Have a helper apply the brakes to stop it, then block that tire with a board or some other block. That will force the other tire to rotate when the brakes are released. Be careful with a block of wood, especially if you use it to stop the tire that is spinning. It can catch the wood and shoot it out.

If you do not see any unevenness in the tread when the tire is rotating, that does not eliminate a broken belt yet. Now you need to look at the grooves in the tread as the tire rotates. When a belt comes apart slowly over a long period of time, as in many months, the entire area will bulge up, but the part of the tread that hits the road can wear down so the contact area looks smooth and even. You have to watch if the grooves show any up and down movement as the tire rotates. That can be rather hard to see. The people at tire and alignment shops are experts at finding that type of thing.

As an alternative, you can switch the two right-side tires, then drive the car to see if the symptom changes. A broken belt on a rear tire will be felt in the seat, but not in the steering wheel. If nothing changes, switch the two left-side tires and drive the car again.

This is not an alignment problem. The alignment affects pulling to one side, an off-center steering wheel, and irregular or uneven tire wear. An oscillating steering wheel and a vibration are caused by parts that are rotating, meaning tires, wheels, and brake rotors.