This might be Islands in the Sky by Arthur C Clarke. This novel is one of Clarke's few juvenile novels.
In the story the protagonist (a teenage boy) wins the grand prize in a quiz show, a trip "to any part of the Earth". He chooses as his destination the Inner Station, which is legally classified as part of the Earth. He spends his time with the apprentices on board the station (teenage boys like himself) and joins in their classes and other occupations during his visit. They have their own spaceship which is described thus:
"I don't quite know how to describe the curious vehicle in which we made the trip. It had been constructed out of junk salvaged from other ships, and was really nothing more than a pressurised cylinder, large enough to hold a dozen people. A low powered rocket unit had been bolted to one end, there were a few auxiliary jets for steering, a simple airlock, a radio to keep in touch with the Station - and that was all. This
peculiar vessel could make the hop across to the 'Morning Star' in about ten minutes, being capable of achieving a top speed of about thirty miles an hour. She had been christened 'The Skylark of Space' - a name apparently taken from a famous old science-fiction story." (Chapter 3)
In terms of your query, it matches:
Golden Age SF story
- Teen Boys
- Living on orbital facility
- build a space ship out of assorted junk
- Hiding it from their parents.
I am pretty sure that the Skylark comes in handy later in the book, but it is a long time since I have read it and I can't find anything on a quick skim of my copy.