As I have said before (or if not I should have!), if Spock was so concerned about an obvious potential conflict of interest (a bit late btw) he should have excused himself from making Uhura's assignment.
I'm pretty sure their relationship was on the DL at that point, for the very reason that Spock is an instructor and Uhura is a cadet. Spock can't recuse himself from such a decision without revealing the relationship.
Uhura had no right to question her posting. There could easily have been a good reason for placing her on a another ship. Besides, if you start by letting people choose their own favourite billets (no matter how "entitled" and full of their own importance they are), where will it end?
She was the most qualified candidate for the post. That certainly gives her the right to question not receiving the post. If
there's a good reason for placing her on another ship (and never mind the counterfactuals: there wasn't
), how is she to know that except by questioning it? Them that don't ask don't get.
And I don't see her as 'full of her own importance', just confident, and justifiably so. She's not some random middle-of-the-road cadet; she's the best in her field and she knows she's the best in her field. Just as with Kirk's "I'll do it in three," any 'entitlement' is explicitly shown to be justified.
As for the alleged lack of 'niceness'... I remember Uhura's pithy "Sorry, neither" when Sulu addressed her as 'Fair maiden' in The Naked Time. To me that seems perfectly consistent with Saldana's portrayal. But others are correct to say that there wasn't very much 'Uhura Prime' to base the reinterpretation on.