I have this. But it happens everywhere, not just in a car. Airplane, my chair getting kicked accidentally, sitting on a moving table at the dentist... also any auditory sound that has a percussive effect, including MRI. But I have other symptoms in addition to exhaustion. My balance, coordination, and capacity for using language deteriorates, my vision gets worse...But exhaustion from motion alone without other symptoms is a new one to me.
I've been offered valium for procedures, but it doesn't help much. Scopolamine patch helped more. This is for motion sickness, so not unreasonable prescription for difficulty for car trips. I guess there are probably other motion sickness treatments.
Car has unique problems, though, in that there can be lots of lights that sometimes flash, sirens and loud sound systems, the stop-start and windy road problems others mentioned, as well as more general travel problems like uncomfortable seats, elevation changes, and acceleration/deceleration.
Sitting in the front seat does help as one can then anticipate what motions the car will make. also the seat tends to be bigger and I can sometimes draw up my legs for a while.
Getting migraine treated helped take the edge off, especially for lights.
I get asthma as soon as I set foot in a car, even if it's been recently dusted, vacuumed, or even shampood. Never understood why.difficulty breathing.