What does the audience learn about Caesar’s character from Act II. sc.ii , and what finally convinces him to agree to go to the Capitol?
Caesar appears in very few scenes in this play that happens to be called Julius Caesar, so it can be difficult to arrive at a definitive description of his character. The scene you mention, Act II, scene ii, is the scene on the morning of his murder, when Caesar must choose between listening to the prophesies and bad dreams of his wife that warn him to stay away from the Capitol and ignoring these signs in order to go forward with his plans.
In the beginning of the scene, Caesar does ask a servant to:
Go bid the priests do present sacrifice
And bring me their opinions of success.
When Calpurnia enters, begging him to remain home, Caesar speaks as if he considers himself invincible. He says that anything that might fright him, "when they shall see/The face of Caesar, they are vanished." He even goes so far as to say that "death, a necessary end/Will come when it will come."
However, to heed the augurers and appease Calpurnia, Caesar agrees to say he is not well and stay at home. So, though he appears to fancy himself invincible, in this moment we learn that he can be swayed by his wife.
Finally, Decius Brutus, one of the conspirators, arrives to convince Caesar to come to the Capitol, which he succeeds in doing. Decius Brutus flatters Caesar's vanity by saying that Calpurnia's dreams merely foretell how important Caesar is to the future of Rome. Caesar is satisfied with this explanation and determines that, after all, he will go to the Senate.
Throughout the scene Caesar seems very willing to change his mind at the drop of a hat. This seems to suit him just fine, since:
. . .danger knows full well
That Caesar is more dangerous than he.
We are two lions litter'd in one day,
And I the elder and more terrible.
Caesar, it appears from this scene, considers himself invincible, and so walks straight into his doom.
In Act 2, Scene 2, Caesar's hubris as his tragic flaw, becomes evident. It is emphasised when he remarks to Calphurnia (who is pleading that he doesn't go to the Capitol), that "Caesar shall forth. The things that threatened me never looked but on my back. When they shall see the face of Caesar, they are vanished." This shows that Caesar feels that he cannot be defeated, or affected by anything around him. This foolishness shown by Caesar, leads to him ignoring importants warning, which eventually leads to his death or tragedy. Caesar's ambition is also evident when Decius is finally able to convince Caesar to go to the Capitol because "The senate have concluded to give this day a crown to mighty Caesar."
in short, he has a big ego.