Complex sentence: While touring Britain to promote the film Chaplin learned that he had been refused a re-entry visa to the United States because of his alleged communist sympathies, and many American theaters refused to play Limelight.
Split into simpler sentences: While touring Britain to promote the film Chaplin learned that he had been refused a re-entry visa to the United States because of his alleged communist sympathies. To add insult to injury, many American theaters refused to play Limelight.