Usually when you feel the shake in the wheel, its an unsprung issue (as in, wheel side of the springs, not car side)
sprung weight issues are usually felt through the floor seat and pedals.
So the first thing you need to do is take the car for a drive on a nice smooth road with the radio off, and pay close attention to what you can actually feel, so you can tell an expert clearly.
In my experience what you describe sounds like a wheel or tyre out of balance, possibly even a wheel bearing (although you would see this immediately when doing an alignment)
Stick your head into the back of the wheel, and see if you can find any evidence of wheel weights not being where they should be.