The Exile: Book 2 of the Greenwood Trilogy

Princess Aeyera has been in exile for 170 years. Now she travels to the Lonely Mountain with a company of dwarves, but there's a problem: she's sworn to protect The Line of Durin. The elves of Mirkwood have turned their backs on her, and though the dwarves of Erebor have accepted her as one of their own, their feelings may change when they find that she is in love with their prince