In The Sound of Music, who is Max Detweiler, a.k.a. Uncle Max? I know he mooches off rich people. That much is obvious. But how does he know the Captain and the Baroness, and why do all the children know him so well that they call him Uncle?
Uncle Max is not actually a blood relative, merely a friend of their father's. In this instance, the 'Uncle' title is an informal title for a close friend.
There's actually more information (that may or may not have any bearing on his role in the story) here: IMDb Bio.
The Sound of Music is loosely based on the first part of the book, The Story of the Trapp Family Singers. In real life, the von Trapps' priest, the Reverend Franz Wasner, acted as their musical director for over 20 years, and the father of the family, Georg, was actually an active participant in the music rather than the strict and distant disciplinarian we see in the film.
The film sought to show Maria as a healing force for the family, so painted the father as remote (much to the actual Trapp family's disappointment). The film creators then needed another character to act as the musical promoter, as the family priest would have been unlikely to act in this role if Georg was not approving. "Max" was a colorful choice, obviously well-known to Georg (he is the only one to call Georg by his first name) and thus able to nudge the father in this direction. His motive for promoting the singing group was money, though he clearly was fond of the family.
The movie does not expressly convey how Max came to know Georg or the Baroness, but simply showed him to be enamored by wealth with the ability to charm his way into the family.