How did the relationship between teens and their parents changed from 1930s to the 1950s?

The biggest difference was child labor laws. Prior to the 50s young people 13 and over were expected to start acting like grownups to some extent, especially to find work and earn some money to amuse themselves. Child labor laws made that illegal, although teens were still able to find work well into the 60s. My father never owned a car in that period because one of his sons always had a car. #2 son even bought a truck for him at one time. #1 son spent $2000 building a car in high school shop class. That is equivalent to a student now spending $40,000 on a project car. A teen could earn that kind of money in those days, and it was not unusual for people to assemble cars from junk parts.

Another big difference was that kids under 13 stayed outside all day. They knew to come home at sundown and that was the only rule. These days parents get locked up for giving a kid that much freedom. People pay lip service to freedom until somebody does something actually free. Then they start saying "Uh oh, we gotta put a stop to that!"