Different babies need different amounts of sleep. Our third child that just turned 2 gave up his morning nap a long time ago. I don't remember exactly, but I think it was about 15mo. This is unusually early, but he seems to not need as much sleep as most babies. (He wakes at 8:00, has a 1 hour nap around 1:30, then doesn't go down for the night until 9:30 or later. But he is usually very cheerful, even with so little sleep.) So you really do have to read your son's cues.
We did have the same issue with the car/stroller when he was transitioning from two naps to one. He usually didn't stay asleep for the transfer to the crib. And then he would be messed up and not be able to fall asleep again until late afternoon, and then would not fall asleep for the night until really late (like after 11:00.) I tried to plan things so that I would not be in the car for more than a few minutes, unless he could sleep for at least an hour in the car. I've eaten lunch, read books and worked on a laptop sitting in the car while parked, sometimes in our garage. There have even been a few times when I moved the babymonitor to the garage so he could continue to sleep in the car while I did chores in the house.
Try to be flexible and creative, and you will find ways to work it out...