My 93 year old father and I were out cruising in my late mother’s Cadillac DeVille. Whenever we reached a speed of 63 mph or faster the car began vibrating, the tires were shaking and so did dad. In the words of Jerry Lee Lewis, there was a whole lotta shaking going on. What do you suggest?
These cars were known to be very sensitive to wheel balance and out-of-round tires. Especially if the engine mounts were worn out. since the car is now 25 years old, I’d say the engine mounts are probably shot.
First I’d take a look at the tires. I’'d guess the car sits a LOT and gets few miles on it, right? The tires are probably very old, likely dry rotted, probably flat-spotted but the tread looks too good to change them, also right? If you want the problem to go away, new tires, properly balanced as a start. If the vibration is still there, have the tires measured and corrected for road-force (ask the tire shop about this. If they don’t have a machine, go elsewhere.
If that doesn’t solve the vibration, replace the engine mounts. Some of them are hydraulic and once the fluid leaks out, things get jumpy.
Good Luck