It's possible the belts inside one of the tires is broken. With brand new tires, likely a manufacturing defect. A broken belt will make the car feel as you describe, and can be mistaken for the tires being out of balance.
I've had this happen before. In my case, the tire was old and I hit too many potholes. One of the unique symptoms I remember is the tire shake will get better and worse by itself sometimes. I think the broken belts are shifting around slightly inside the tire, and when they get in a "good" position the shaking will be less, and when the belts move around again the shaking will get worse again. This can repeat.
Since you feel it strongly in the steering wheel, it is more likely a front tire. To diagnose, you could replace one of the front tires with the spare, and test drive to see if the shake goes away completely. If it does, you found the bad tire. If not, try swapping the other front tire and see if the shake goes away. The normal warnings about not driving too far or too fast on the spare tire apply. You said you feel it even at low speeds, so that makes it easier to test drive and maybe figure it out.