Did they check the engine mounts? Maybe one or more are loose or broken.A long time ago I had a 64 Impala.Every time we made a left hand turn it made a awful noise.Turns out the engine mounting bracket on the right hand side was broke so when we made a left turn,the engine came up enough to hit the hood...just a thought...good luck!
It could be having a misfire in the engine.
Can a disfunction on the timing chain cause engine shaking?