Good luck. Could be many things but hopefully an easy fix - alignment - poor tire wear (do you rotate every 3-5k miles) - incorrect torque on suspension bolts, bent sway bar.
Question: how bad is the shake? When I used to get mine it was bad - could not even hang on to the steering wheel bad - and always had to come to a complete stop before it went away. Luckily only happened a couple times and was when I put on a lift and 35s. However, it was always caused by a pot hole or larger bump, never just came on.
As stated go to another dealer and hopefully they can pin point the issue. It will show in the system that you were at another dealer previously for the issue when they run your vin so don’t get caught in the lie game that they play.
Hope it all works out.