Ask the tire shop to also check for broken radial tire belts
, tire tread separation
, and flat spots or uneven tread wear while they're checking wheel balance. Those can also cause wheel shaking. I just went through a similar troubleshooting process with our '03 base Vibe and found this link
helpful. I started with the snow-in-wheel theory (we're in Michigan), then graduated to checking for missing clip-on wheel weights, signs of a broken radial tire belt or separating tread, and uneven tire wear.
After I jacked up both front wheels and put the car in drive so I could observe the tire tread while spinning in the course of checking for separated tread or a broken belt, I found that the passenger front wheel wasn't spinning at all. Turned out to be a bad caliper, frozen so tight that it was causing the steering wheel to vibrate while moving.
Caught me off-guard as the shaking was happening all the time, not simply when applying the brakes and there wasn't any of the tell-tale signs like pulling to one side when braking or excessive dust coating the wheel. I had also proactively replaced both calipers in 2016, about 30,000 miles ago when replacing pads and rotors. The new Duralast remanufactured units turned out to be junk, the other side wasn't yet frozen completely but it was starting to stick.
Thankfully, AutoZone honored their limited lifetime warranty. Just finished replacing the old calipers with A-1 Cardone units from Rock Auto which carry a 10 year, 100,000 mile warranty and come powder-coated for rust prevention. Vibration and steering wheel wobble gone!