It could be a shifted belt in one of the tires.
Low speed problems like that are usually either a bad tire, bent wheel or a problem with CV joints.
At low speed: Damaged or failed tire, bent wheel, damaged brake, damaged axle. Dangerous failure of a wheel bearing. At high speed generally a wheel balanace problem. While braking a bent or warped brake component.
Tire out of balance, bent wheel, defective tire, worn suspension or steering parts. Have the tires balanced, and all parts inspected.
The steering wheel wobbles, because of the unconditional pressures from the ground that is adjusted at speeds when it reflects gravity.
You probably need to get your tires balanced. Or replaced. If the bias goes (steel belt breaks or shifts), the car will waddle at low speeds, and the steering wheel will shake at high speeds.
Unbalanced wheels or a bent track rod
You might possibly have a bent drive shaft, or if you have oversized tires they could be rubbing against the wheel wells
Means your steering wheel pump might be going bad. But first check your steering wheel fluid you could be very low.
When the car is driven at low speed, the power steering gives full assist so the driver can turn the steering wheel easily. Parking or turning tight corners can be done with little effort. As vehicle speed increases, the mount of power steering assist is reduced and the steering wheel becomes harder to turn. This gives the driver more feedback about road conditions through the steering wheel and better vehicle control. If an emergency arises and the driver needs to turn the steering wheel quickly, the full power assist is provided almost immediately after the wheel is turned only a few degrees.
Tires,inner tie rod bushings, if the steering wheel shakes when brakes are applied - brake rotors warped.
Low steering fluid can cause a steering wheel to whine when turning. A worn steering belt can also cause a steering wheel to whine when a car is being turned.