As for Rhaenyra Targaryen, she grew up believing she would rule Westeros. But when the time came, her enemies and family stole the crown from her. She answered with fire and blood and was destroyed by them. So while Rhaenyra may have been the first woman to claim the Iron Throne, she never ruled the Seven Kingdoms.
However, in the episode, Rhaenyra was simply coronated with her father's crown and in doing so became the Black Queen. In Fire and Blood by George R.R. Martin, Rhaenyra does indeed take the Iron Throne and become queen over the Seven Kingdoms, however, her reign is short-lived.
Rhaenyra does everything to prevent war, until the end
After the somber ceremony, Ser Erryk Cargyll (Elliott Tittensor) produces the crown of King Viserys, swearing fealty to Queen Rhaenyra. Daemon himself places the crown on her head and bows to his wife, saying "My queen."
No, Daemon Targaryen never becomes king.
The closest he ever comes to the title is 'prince consort' when Rhaenyra is crowned queen. The reason why Daemon doesn't become king when his wife is queen probably comes down to George RR Martin basing his monarchical system on the English monarchy.
As Joffrey tells us, eventually, Rhaenyra's half-brother Aegon Targaryen will feed her to his dragon Sunfyre. She dies as her son, Aegon III, watches. That's the bullet point version. Of course, there's a lot that happens between the end of House of the Dragon season 1 and Rhaenyra's death.
With both Rhaenyra and Aegon gone, there's one clear person to inherit the throne: Rhaenyra's son Aegon, known as “Aegon the younger” in the books (her older sons had all died by this point).
The war ended when Aegon II died in 131 AC with no male issue, and was succeeded by Rhaenyra's and Daemon's elder son, the boy Aegon III, who had seen his mother's death by dragon.
Laena and Daemon marry soon after. Laena and Daemon were a power couple, and their marriage was celebrated by nearly all of Westeros and Essos — except for King Viserys and his court, who considered it another sign of Daemon's disrespect.
According to the accounts of Septon Eustace, prior to her turning sixteen, Rhaenyra lost her virginity to her uncle, Prince Daemon, after he seduced her.
Rhaenyra Targaryen, the rightful heir to the Iron Throne, briefly considered bending the knee to her half-brother King Aegon II in the Season 1 finale of House of the Dragon, thus sparing the citizens of Westeros years of dragon fire and bloodshed.
Comparatively, Rhaenyra receives her coronation in a private ceremony as she mourns the death of her stillborn child. These dueling sequences signify the types of rulers that they will become.
With no one left to help her, Aegon II demanded his dragon Sunfyre to kill and then consume his older sister right in front of the eyes of her last remaining child and future king, Aegon The Younger.
Eventually, Rhaenyra is killed, as is Aegon II, meaning both major claimants to the Iron Throne are dead. As Aegon had no heirs, the Iron Throne fell to Aegon III, Rhaenyra's firstborn son with Daemon Targaryen.
Rhaenyra's eleven year-old son, Aegon the Younger, was crowned king, and married to Aegon II's daughter and only remaining child, Jaehaera Targaryen, uniting the claims.
Rhaenyra Targaryen (Emma D'Arcy) and Daemon Targaryen (Matt Smith) finally had sex on House of the Dragon. After teasing their deep connection for weeks, making out in a brothel, and flirting their way through King's Landing, uncle and niece at long last did the dirty.
Viserys II Targaryen was the tenth Targaryen king to sit the Iron Throne as Lord of the Seven Kingdoms. He was the son of Rhaenyra Targaryen and Daemon Targaryen, the brother and Hand of King Aegon III Targaryen, and the father of King Aegon IV Targaryen, Queen Naerys Targaryen, and Prince Aemon "the Dragonknight".
Some dragon-like babies are born after incredibly complicated and anger-induced births, so it's possible that the fire of the dragon being released within both Rhaenyra and Syrax during the birth somehow impacted her daughter's physical characteristics.
Daemon couldn't perform with Rhaenyra after she took control of the situation. “It's the idea that Daemon is using Rhaenyra as a way to get at her father,” showrunner Miguel Sapochnik said.
While House Of The Dragon episode 4 showed Daemon was able to seduce Rhaenyra by kissing and undressing her, he couldn't fulfill the act due to impotence.
Turns out, Rhaenyra and Daemon are endgame, meaning they have a sexually tense relationship, eventually hook up, and get married—which is pretty significant from a power play perspective considering (1) they both want the throne and (2) their Targaryen union is almost sure to guarantee that happens—even though Alicent ...
Daemon shows his genuine care and attention to Rhaenyra several times before the two marry. This doesn't take away from the many destructive and inappropriate parts of their relationship, but the books imply that Daemon does love Rhaenyra.
In George R.R. Martin's fictitious history of the Targaryen family, we learn that Rhaenyra does eventually have children with her uncle Daemon: two boys named Viserys II and Aegon III, both of whom eventually become king.
Having already lost her first three sons to the war, Rhaenyra fled back to Dragonstone for safety. But there she was betrayed and brought before her injured and delirious brother King Aegon II. So how did Rhaenyra Targaryen die? Well, Aegon had his dragon Sunfyre burn Rhaenyra alive before he ate her.
Princess Rhaenyra rules as Queen Rhaenyra for about half a year on the Iron Throne. As many of her children are killed, she flees King's Landing after a riot known as the Storming of the Dragonpit, and is eventually caught. Her half-brother, Alicent's son Aegon II, feeds her to his dragon, Sunfyre.
Aemond killed Rhaenyra's son after a dragon chase through the rain, before which Aemond laughed and tried to cut out Luke's eye. The pursuit culminated in Aemond losing control of his dragon, which brutally chomped Luke and his dragon.