Much of the third episode of 'House of the Dragon' was centered around Rhaenyra Targaryen's inevitable nuptials. Being the stubborn, powerful girl that she is, it's no surprise that she was resistant to the idea. Rhaenyra is picky. She doesn't want to be lorded over, and she wasn't about to be pawned off to a drunken Lannister. But in the books, she does end up marrying, and the story is quite interesting.
Ser Criston Cole Courtesy of HBOmax
The bond between Rhynaera and Ser Criston was obvious from the beginning. The two seem to be a well-matched pair. According to some accounts, they do eventually fall in love. It's said that when Rhynaera is promised to another, Criston sneaks into her bed chamber and confesses his love to her. He asks her to run away with him to the Free Cities, where he could work as a mercenary. She refuses, saying that a queen can't be married to a sellsword. They never marry, but she does seem to regret this later.
Laenor Velaryon Courtesy of HBOMax
When it comes down to it, Targaryens prefer to keep it in the family. The king's advisors had long suggested a union between the Targaryen and Velaryon houses as a show of unity for their shared ancestry. They eventually get their way when Rhaenyra is matched to Laenor, her cousin. Of course, things don't go the way they're supposed to. Laenor was said to spur women and surround himself with beautiful young men instead. Their three sons were said to have been fathered by her sworn shield, Ser Harwin 'Breakbones.' Laenor is eventually murdered at a fair. It's said that Rhaenyra's next husband might have had something to do with that, and nobody would be surprised if he did.
Rhaenyra and Daemon Targaryen Courtesy of HBOMax
Targaryens are fated to be with Targaryens, but this match is different. Daemon has so far been slated to be the bad guy of the series. He is a scorned, would-be heir with a vengeful streak, who stole one of the family's dragons and a prized piece of land for his own. But he wasn't willing to kill his niece when he had the chance. In fact, he has a soft spot for her that eventually blossoms into a loving marriage, children and all. He even defends her in the upcoming conflict.
Courtesy of HBOMax
'The Game of Thrones' and A Song of Ice and Fire were very different beasts. HBO didn't remain true to the books, and George R.R. Martin never allowed the show to confine his creativity when he was writing new installments. The truth is that this current iteration of Rhaenyra is still very young. We don't know what's going to happen to her yet. All we see is her blossoming romance with Ser Criston, a spurned and drunken Lannister, and the distant proposition of marrying Laenor.