2002 Toyota Corolla can't go safely over 45 mph.

I'm sure a good local garage can find the problem. Be it unbalanced tires or a bent wheel, to engine misfires.

I'm betting on a rotational problem like a damaged wheel. Since nothing changed when you had a shop look at it, wheel balancing was not the issue. I would have them remove wheels one at a time and look for one that is out of round.

I'm going to guess....that it only shudders on gentle acceleration at that speed, and that if you step into it you dont feel it. As well as it not doing it when you let off the gas pedal?

Thank you all for trying. As I mentioned this problem has been there since 2002. Repeated visits to the dealership and other mechanics over the last 18 years have not found the cause. Literally, when the car hits 50 mph is starts shuddering and feels like it will fall apart. Thankfully I live in a rural area and can keep it under 50 mph.

Question....can you feel what corner of the car its doing this in? And when it does, are you able to SAFELY determine what direction it pulls?

It seems to be from all over under the car.

And I'm going to guess in that time you've had brake calipers, u-joints, wheel bearings, axle all checked, transmission flushed, new transmission filter, alignment checked and no misfiring?