A shimmy usually started by the toe-in being too far toed out.....( But not always, or is not the only contributor.)
And then allowed to continue by looseness in the steering. Once it starts, the usual cure is to slow down to well below the speed that it started at and then to sneak the speed back up to just below where it started at. I have never seen a case where increasing the speed, made it better.
What is happening is the toed-out tires are taking off at an angle to the road and not straight ahead. Of course that is only possible until the tire cords reach their limit of elasticity, and then the tire unloads and they try to snap back to the straight ahead position. And for a split second they do, but the tendency of a FWD car immediately toes the steering in again, and so it repeats endlessly, Scrubbing the rubber off.
The wet road reduces the traction of the tire, and so the shimmy is temporarily reduced.
Honestly your tech should know this. Find a new shop.
With the tires being driven in one direction by the power-unit, and in another by the alignment, the cords are under a lot of stress,flexing, and creating a lot of unnecessary heat. And heat kills tires fast. Jack the pressure up a good 5 psi over the recommended until you get this sorted.
