How did personal relationships between Marc Antony and Cleopatra affect the history of the roman empire?

As you know, at the time of Antony and Cleopatra's "relationship", Antony was involved in a power struggle with Octavian. Their personal affair gave Octavian fuel for his propaganda engine, especially since Antony was married to Octavian's sister while carrying on with Cleopatra. But it was their political ambitions that worried Rome more. After things boiled over into war and Octavian became sole ruler, he was able to change the system of Roman government. What some people erroneously call the "Roman Empire" was established.