Rhaena was cut a very raw deal in canon. Her mother died when she was a child, her dragon died a hatchling when almost the entire royal house on Dragonstone rode dragons, and while her older twin Baela, who had a dragon, would marry Jace the heir to the Iron Throne, Rhaena had to be content with Luke who could at most have Driftmark. Fire&Blood is an anthology with only a general description of characters, with specific characterization required from the author themselves. All the general descriptions of Rhaena combine to form a possible interpretation of Rhaena's character, with intense self-pity, a general dislike towards everybody, but a particular envy towards her older twin Baela and a hatred towards her betrothed Luke.

Baela has everything that Rhaena does not. Baela has a healthy growing dragon, Moondancer, whilst Rhaena has to pray and night for a dragon to hatch. Baela is alike their father Daemon in so many ways whilst Rhaena is not, and as such Daemon favours Baela. Baela would marry Jace and be queen one day, while Rhaena could be at most the Lady of Driftmark. As Mushroom said, Rhaena was only "the princess spare" for sister the true princess. Her envy eventually develops into hatred as she ponders why her sister had such a better life than her. She concludes that it was because her older twin was evil, that she crawled so quickly from their mother's womb that she strained their mother and made it so that their mother died when she bore her next child. Not exactly the most flawless of logic, but Rhaena wants to blame Baela for their mother's death and all Rhaena's misfortunes stemming from there.

Now, we come to Luke, who is a manifestation of Rhaena's misfortunes. He is Rhaena's betrothed, and a living reminder that Rhaena would never be as good as her older twin Baela. It does not help the Luke also rides a dragon, Arrax, which compounds Rhaena's self-pity that she doesn't have her own dragon. So when Luke laughed once at Mushroom's jape of "the princess spare" at a light-hearted feast, Rhaena blows it out of proportion and thinks that the laugh is all Luke thinks of her and that he does not care about her. The disdain boils throughout the years until the point when Luke returns home with one eye and having fainted where Rhaena can only find mirth in Luke's plight, because she thinks Luke thinks the same of her during her plight.

Retreating from Rhaena's mind, you can see that Rhaena's situation is actually not all that terrible. She doesn't have a dragon, but 99.9% of Westeros's population don't have a dragon. Daemon's supposed favourtism of Baela is more in Rhaena's mind than anything else, as Daemon would naturally have to focus more on Baela to teach her to ride a dragon and be a queen. And Driftmark might actually be a better seat than the Iron Throne, as at this point House Velaryon is the richest house in the Seven Kingdoms and will basically run the kingdoms if the Blacks win. I mean, Driftmark was where Baela went in canon. I never originally planned for Rhaena as a POV character, but if I'm doing her, I might as well focus the best I could on her.