For Caesar, you can show his ambitious side not just in politics but also in his relationship. He could be determined to make Cornelia the happiest woman, seeing it as another conquest. For Cornelia, emphasize her intelligence. She can be the one who gives Caesar good advice on political matters from time to time.
Julius Caesar's story is based on actual history. While some details might have been embellished or simplified for storytelling purposes, the main events and his existence are factual.