Even Laenor, Rhaenyra's husband, hints that he knows the princes are not biologically his children in Episode 6. Despite the seeming acceptance of the children's true parents, whispers in the Red Keep intensify following Harwin's fight with Criston, the latter of whom teased the former about his secret fatherhood.
Rhaenyra and Daemon both know Laenor is alive, and faked his death.
During the civil war called the Dance of the Dragons (129 AC - 131 AC), Laenor's three sons by Rhaenyra all died. However, during the Sowing of the Seeds, Marilda of Hull brought forth her two sons, Addam and Alyn, claiming them to have been Laenor's bastards.
Jacaerys, Rhaenyra's eldest son, and his two younger brothers have spent their short lives surrounded by whispers that their real father was Ser Harwin Strong. It's an open secret that these “strong” boys aren't the sons of Laenor Velaryon.
Rhaenyra was perfectly capable of having kids, and she had five healthy sons. Laenor didn't have children because he didn't want to, not because he was incapable (as in he was impotent, sterile, or had a condition that lowered his ability to sire children, such as undescended testicles, hypospadias, or chordee.)
It isn't explicitly stated in the show, but because we learn after episode six that all three boys have dark brown hair — and despite Rhaenyra and Laenor's matching blond color — it has been strongly implied that they are actually the children of Ser Harwin Strong, the Lord Commander of the City Watch.
It was clear that Leana and Laenor had a close relationship, and she likely would not appreciate her uncle choosing this moment to make a statement while her brother grieves. Daemon laughs at this moment because Vaemond is choosing this moment to guilt Rhaenyra for having children with Harwin Strong (Ryan Corr).
Even Laenor, Rhaenyra's husband, hints that he knows the princes are not biologically his children in Episode 6. Despite the seeming acceptance of the children's true parents, whispers in the Red Keep intensify following Harwin's fight with Criston, the latter of whom teased the former about his secret fatherhood.
Ser Laenor and Princess Rhaenyra had three sons, Jacaerys Velaryon, Lucerys Velaryon and Joffrey Velaryon. Although due to the traits of these three, and Laenor spending very little time with Princess Rhaenyra, it was clear that Jacaerys, Lucerys, and Joffrey were not his children.
Like Laenor Velaryon's sexuality, it was a “known secret” in the Red Keep that Harwin Strong was the father to Rhaenyra's three children: Jacaerys, Lucerys, and Joffrey.
Rhaenyra Targaryen: In episode 2, Viserys mentions his daughter, Rhaenyra, is 15 years old. Then, following a time jump in episode 3, he mentions she is now 17 (and “of age” to marry).
Rhaenyra's second son with Prince Daemon would also later rule as King Viserys II Targaryen, as both sons of his brother Aegon III, Daeron I and Baelor I, later died without issue.
Rhaenyra has had a tough couple weeks. First, she finds out that her half-brother Aegon II has usurped the throne and that she will have to fight for her claim as queen. Then, she gives birth to a stillborn child. And finally she loses her second eldest son Lucerys to a dragon battle.
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).
In George R.R. Martin's book Fire & Blood, we are told of the incident where Rhaenyra Targaryen's husband Laenor Velaryon dies while attending a fair in Spicetown, on the island of Driftmark. We learn he was “stabbed to death” by a knight in his father's service, his paramour Ser Qarl Quarry.
Since Daemon's body was never recovered from the Gods Eye, singers say that he lived to spend the rest of his days in secret with Nettles. Daemon never achieved his ambition to sit on the Iron Throne, though his sons Aegon III and Viserys II eventually did.
Born in 114 AC, Jacaerys Velaryon is the firstborn son of Princess Rhaenyra and Ser Laenor. Even early on, Jace quickly proves that he is a valuable asset to the war pursuit against his uncle Aegon II. Jace flies as an envoy on his dragon, Vermax, gaining the support of the Vale, the Three Sisters, and the North.
Rhaenyra and Laenor are also only second cousins. That's an admirable match for House Targaryen.
Jacaerys Velaryon Is Rhaenyra's Firstborn Son and Heir
Firstborn son of Rhaenyra and her first husband Laenor Velaryon, Jacaerys was affectionately known to his family as Jace.
The Velaryons Are Dragonriders Thanks to Rhaenys Targaryen
So far in the show, Laenor Velaryon, who rides Seasmoke, was already mentioned by Lord Lyonel Strong (Gavin Spokes) to be of pure Valyrian descent, but he is also a dragonseed.
Rhaenyra's children are bastards, and Vaemond finally let everyone know in Episode 8, as loudly as he possibly could.
Laenor also happens to be black, adding further mystery to the children's appearance. House of the Dragon quickly explains the anomaly, revealing the boys were the result of Rhaenyra's affair with Ser Harwin Strong.
It was abundantly clear in the season finale that Daemon truly values Rhaenyra as the queen, and it doesn't appear to be for his own gain. All of his actions indicate that he looks to her as his leader even before she's taken power and has every intention to get her to her rightful throne.
As clarified on House of the Dragon Inside the Episode, the answer is two-fold. They showed one reason back in episode one when Daemon had problems finishing in the bedroom with Mysaria. Daemon struggles with impotence. This may also be why he has fathered no children with his wife.
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.