George Sears Green (1801-1899). Source
David W. Palmer, The Forgotten Hero of Gettysburg: a Biography of George Sears Green. (Bloomington IN: Xlibris, 2004).
Edit - A number of players named James Barnes and provided sources in support of that answer. He does satisfy several of the clues, but though Barnes did serve at a number of battles and his son did command a number of vessels, the sources do not appear to support the contention that Barnes deserved credit for winning a well-known battle or that his son commanded a famous ship.