The "authorized version" can thus be summarized: As one of the leaders of the rebellion of the Noldor, Galadriel falls under the Ban of the Valar. Not obeying the Valar by not returning to Valinor at the end of the 1st and 2nd Age, Galadriel shows pride and she still seeks dominions of her own and thus the Ban stays in place. It has even been suggested that having been a leader of the exodus of the Noldor, the Grace of the Valar was withheld from her. Only by passing the test, refusing Frodo's offer of the Ring, she is finally pardoned and allowed into Valinor.
But Galadriel behaves rather oddly for one so treated by the Valar, doesn’t she? Right from the start of the 2nd Age, she does nothing to chase honour or glory for herself, seeking no dominions at all, but she works only to thwart Sauron and his minions and plans. In the 3rd Age she forms the White Council, showing odd authority for one banned by the Valar. The dominion she finally accepts happens to overlook Dol Guldur, the biggest source of evil at that moment.
But it is in crucial pages of The Lord of the Rings that the really urgent questions are raised. How does Galadriel know that Gandalf is sent back by the Valar? Seen in her mirror? Not likely, for how can she look for somebody she cannot know to be there? Telepathy? Less likely, because Gandalf is barely conscious. More importantly, by what authority can Galadriel order about the mighty eagle Gwaihir, minion of Manwë? And finally, the Phial. Admittedly, catching the starlight of Eärendil in a bottle can be acknowledged to be an Aulëan technique, which she had learned in Valinor. But it is certainly the light of Varda herself that shines into the eyes of Shelob when Samwise invokes her name. Shelob would not have been demoralized by any lesser light.
It would seem the Valar have been oddly benevolent and cooperative to one they allegedly banned.
The conclusion imposes itself that Galadriel stays in Middle-earth by the implicit benevolence of the Valar, and probably on their explicit mission. Could the authorized version of the Ban have been meant to keep Galadriel's role hidden from Sauron, to add to the stealth of her works as a champion for Aman?
But maybe, quite simply, the Grace of the Valar was bestowed upon her, but being who she is, she felt she should do something to deserve it. She didn´t want to be allowed into Aman as a pardon, but to earn the right.
Psychologically the Prophecy of the North, the Doom of the Noldor, was of the utmost importance for Galadriel's motives and decisions. In the end she had come to understand perfectly both the opportunities and limitations of her powers and role. Never could she seek domination or glory, only by aiding the choices of truly free peoples (and by the Prophecy she was not free) could she succeed. She herself was bound; she herself could and should not seek to fight Sauron directly..
There can be no doubt what would have happened if she would have accepted Frodo's gift of the Ring. In Middle-earth, there existed only two beings who could hope to be her match, and of the two: Gandalf would have had no choice but to retreat before her because he must admit his mission failed. The other, Sauron…all his innermost plans and thoughts would have been laid bare before Galadriel, wearing his Ring. She would have overcome him with ease. So she would undoubtedly have "won", and thereby would have been lost and the world with her. Because as sure as Galadriel was that with the Ring she would overcome any other, she was sure that the Ring would overcome her. And only by this certainty, won by many years of witnessing the workings of the Doom of the Noldor, did she take the right decision.
Still, Galadriel could never be certain that all would end as it ended. Quite probably, in her mirror she saw success as a mere contingency between many Paths of Doom. She - but also Frodo and Sam and Aragorn and Faramir and many others - had to pass crucial tests. And in that way her song of Farewell to the Fellowship may quite well have been a plea to Varda for aid and mercy. For Galadriel there were in the end but two choices: Valinor or failure.
JRR Tolkien: The Lord of the Rings<>Ed. Chr Tolkien: Silmarillion
 Cf. Chr. Tolkien’s comments on p. 321 of History of Middle-earth, Vol. XII, The Peoples of Middle-earth.
 Even the most fierce critics should admit that Peter Jackson and Cate Blanchett did great credit to the persona of Galadriel in the movie trilogy. Small aberrations – as with some of the conversations, her gifts to the Fellowship, Galadriel’s absence at the wedding of Arwen, Celeborn’s presence on the Last Ship – should be overlooked. But Galadriel's urging Elrond to send Eldar to the aid of Helm’s Deep is in my opinion a fault. For by so doing Galadriel would still not have fully understood the implications of the Prophecy. But she did, so she would not have done any such thing. On the other hand, the non-interference of the Eldar in the War of the Rings has raised many questions even for many readers of the books, let alone the audience of the movies. Questions that cannot be possibly answered within the timeframe of even the extended movie trilogy. So the fault can be forgiven.