When I was 2, my parents , our dog and I traveled from Omaha to Los Angeles in the TR3. That's a couple thousand miles I would guess. Back then (1969), there was no talk of safety. It was just another car (although a very cool car), and if you had to haul your kid somewhere in it, you did it.
By the way, I don't remember one moment of it, and there is no chance I would do that today. My kids are 6, 8, and 10, and I do take them out for drives, but I stay off the main roads as much as possible.