Why would the steering wheel shake back and forth while driving and only at low speeds?

You should take the vehicle to the tire store where you purchased the front tires. Your description sounds a lot like either a slipped belt or a bent wheel.

I'd bet on the slipped belt. Radial tires have a very flexible sidewall (radial ply) and a less flexible and tougher tread ply, called the belt. If the material between the belt and the radial plies separates, it will typically slip to one side and only in limited areas of the tire.

One way to check for yourself, jack up the front end and spin the tires. Watch for an area that suddenly goes off to the side. If you see that, it's a slipped belt, and if you have a slipped belt, don't take the vehicle on the freeway and definitely get the tire replaced as soon as possible. They're very dangerous.