What-If? Empress Cleopatra of the Roman-Egyptian Empire

What-If? Empress Cleopatra:

The death of his daughter Julia had brought about a change in Caesar, one where he sought to distance himself from the pain by focusing ever more on his work. This change is enough that he (temporarily) neglects his familial duties and does not remarry, despite the attempts of others, meaning that by the time he arrives in Egypt, Calpurnia has already been wed to another.

It is here, while Caesar is siding with Cleopatra in the dispute between her and her husband Ptolemy, that she spots a vulnerability to her savior. After quite some time, she manages to convince Caesar of the benefit of a Personal Union between Rome and Egypt, solidifying Caesar's position as both Dictator of Rome and Rome's hold over Egypt.

Assuming that this occurs, what changes? What stays the same? Does this event accelerate Caesar's death in the Senate? Does Caesar's now legitimate son Caesarion (with possiblly a different name such as Alexander), take Octavian's place as future Emperor of Rome?
 
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