(This is an incomplete summary of a shiur from R' David Fohrman which I thought interesting. His book on Breishit is interesting as well.)
Three things are mentioned about the appearance Vashti was supposed to make at Ahashverosh's party. 1) She was to show off her beauty. 2) She was to wear a crown. 3) The audience was the assembled princes of the empire.
This strange request can be understood as follows. Vashti was a living symbol of the Persian empire - like the Statue of Liberty is nowadays for the US. Like in modern advertising where beautiful women are displayed to market cars or soft drinks, Vashti wearing a crown was shown off to market the beauty of the crown and the Persian empire. When she refused to do this, she implied that the empire had no beauty to show off. Thus Ahashverosh became so angry at her.
Vashti's replacement was supposed to fix her flaw, and successfully represent Persia. For this purpose, the replacement had to be identifiable as Persian. Mordechai asked Esther not to mention her origin. Precisely because she had no discernable non-Persian identity, unlike residents of the other 127 provinces, Ahashverosh was able to choose her as representative of the kingdom.
When Haman's decree became know, Esther was presented with a dilemma. If she spoke up on behalf of her people, she would lose the "non-ethnic" quality which was why she became queen in the first place. Thus, she did not directly request this, even when Ahashverosh promised her "up to half the kingdom". Instead, she attempted to trap Haman, and thus to get both him and his decree removed.
She was half-successful in this. Haman was discovered on her bed, but was immediately killed, before Esther could ask for any decrees associated with him to be revoked. Now Esther's only option was to ask directly for the decree to be revoked.
At this point, for the only time in the Megillah, she fell at Ahashverosh's feet and cried and begged. Despite this display of emotion, Ahashverosh refused! He did not divorce Esther for declaring her identity, but neither did he grant her request. He only allowed for a parallel decree to be issued allowing the Jews to defend themselves. Luckily this was enough, and the Jews lived happily ever after.