Complex sentence: In 1904 the band became even more well known when it played at the National K.P. encampment in Louisville, Kentucky, and stopped off en route, by invitation, to play at the World's Fair in St. Louis.
Split into simpler sentences: In 1904 the band played at the National K.P. encampment in Louisville, Kentucky. En route, it played by invitation at the World's Fair in St. Louis.