Let's see what was needed to make sure the LRV didn't disintegrate during launch. These are the same requirements that apply to the rest of the Saturn V stack, by the way.
- You have to know what the environment will be. This is initially done by testing individual stages and the entire rocket: early launches are instrumented to measure noise, vibration and acceleration.
- once you've done this for one rocket, you can develop models that help predict what the noise and vibration will be for your new design.
These days, noise and vibration data is published in a rocket's user manual. In the linked Ariane 5 user manual, chapter 3 lists the environmental data:
- steady-state acceleration
- regular and random vibration
- electromagnetic interference
Space agencies have test chambers that can simulate this environment. Computer simulation is also possible these days.
Once you know the noise and vibration environment, you can design for it. Noise and vibration exert a known load on a structure, you just have to make the structure strong enough to withstand this load.
The assumption that a car would not survive launch is incorrect. Cars are subject to noise and vibration analysis during development (to ensure passenger comfort and durability of the car), and SpaceX would have easy access to that data for a Tesla car. Even without that data, they will have put the car through noise and vibration testing (just like any other payload) because you really don't want bits dropping off and damaging the launcher.