I'm not exactly clear on why the coffee would splash out, but if you arrange everything just right so that the final, tilted surface is just at the lip of the cup, then the surface should act as a damped pendulum, and slop a bit on the first few cycles of its oscillation. Is this what you had in mind?
The situation where the car "jerks forward" sounds different. It sounds as if the acceleration of the car is not constant (which is how real cars accelerate). But that's not a fair test of the equivalence principle, that's just a test of the mechanics of the car and driver.
In order to compare this to the gravitational field case, you'd have to have some way of "turning on" the mass behind the car. I don't know of any way to do this, so yes, the fact that you can turn a dynamic acceleration on and off rapidly would probably be a good indication that the acceleration was not gravitational in nature. But this isn't a violation of the equivalence principle: the equivalence principle is a statement about constant, uniform accelerations.
The damped oscillations of the coffee surface wouldn't constitute a violation of the equivalence principle, because that just tells you that the surface of the coffee was tilted somehow with respect to vertical in the recent past. If you tilted it somehow by the same amount in a gravitational field, and then let it go to find its equilibrium state, it would behave in precisely the same way, and slop the same amount.
In a real experiment, there would be better ways to distinguish between the car's acceleration and the gravitational field. For example, any real gravitational field will have some measurable divergence--the tidal force--whereas the car's acceleration will not. But this also is not considered a violation of the equivalence principle. It's just a feature of the specific experimental geometry, an "in practice" distinction rather than an "in principle" distinction.
That is exactly the distiction I was making: between the way real cars on earth accelerate and the equivalence principle. I wan't trying to disprove the equivalence principle. It's two different scenarios.
I don't know of any way to do this, so yes, the fact that you can turn a dynamic acceleration on and off rapidly would probably be a good indication that the acceleration was not gravitational in nature.
That was the distiction I was making: between acceleration due to gravity and acceleration due to some other force. That is all I was trying to do.
Since you have joined in, do you think Super String theory in on the right path to reconcile the contraditions between quantum mechanics and relativity?