'Mozart led a pretty rough life, and only wrote one piece in a minor key.'
Can you clarify about this minor key claim, Mozart wrote in a minor key much of the time, so this claim is puzzling to me. Whether he wrote in major or minor had little, if anything at all, to do with his personal life.
Although Mozart was broke most of the time, he typically had money coming in due to the self promotion of his concerts, his private commissions and his posts to the courts. He was employed nearly all of his life. Mozart was just notoriously bad at saving money but compared to his contemporaries, he did pretty well financially. What Mozart did suffer from was an insecurity of self image due to his having been scarred by small pox from an early age.