How to do this is difficult. I've thought of doing something along these lines as a what if, and could never get a plausible POD.
In the abstract, I think you could get a situation where the internal combustion engine is used almost purely for commercial and military use, and not for personal use by ordinary civilians, unless they are ridiculously rich. The situation would be analogous with that of planes today, used by the military, for freight travel, by commercial airlines to ferry masses of people, corporate jets, and personal airplanes for the wealthy, but we don't have a "Jetsons" situation where everyone uses their airplane to get to work or the mall.
However, to get this with ground transportation, you need to either make cars as expensive as airplanes to build, operate, and maintain, or have their use restricted by an autocratic government. The first would probably require a geologic POD where the Earth as a whole is just poorer with less fossil fuels and metals. You might do it with an industrial revolution that is cut short for some reason, so vehicles with internal combustion engines exist but can't be reproduced.
The autocratic government is a little easier. There is an argument that the internal combustion engine is so valuable that it should be limited to military and agriculture, and OK we will allow some trucks and rich and well connected people to own them. The peasants can take the bus. To my knowledge, no one, not even Russia or China, ever thought of trying that. The Nazis even went out of their way to produce cars to the masses.
The United States has banned easily manufactured, widely available, and popular products before, even to the point of shutting down entire industries, namely recreational drugs, including alcohol for fourteen years. However, this was done for quasi-religious reasons, and to get cars under this umbrella you need some sort of POD where the notion that moving away from your home town is somehow sinful gets ingrained in whatever religion Americans claim to believe.