Complex sentence: Corré's big break came in 1937 when she was invited by Hughie Green to join his touring all-children concert party "Hughie Green and his Gang", which played until the outbreak of World War II in 1939.
Split into simpler sentences: Corré's big break came in 1937 when she was invited by Hughie Green to join his touring concert party "Hughie Green and his Gang". With a cast entirely made up of children, the company toured until the outbreak of World War II in 1939.