I'm testing in scenes without UI, and the problems persist.
I've found that one cause of the issues is the VPHeadMotion component. This component creates a very light ridigbody and attaches it to the vehicle with a joint. Translating the vehicle doesn't seem to translate the child rigidbody, so the joint enforcing the constraint causes the vehicle to spin. This is not the only cause of issues, so I'm investigating this further.