I wonder how the laws of succession work over there?
Aerys II is King and has a son and heir Rhaegar. Rhaegar annuls his marriage to Elia Martell and marries Lyanna Stark. Lyanna gives birth to the person we know as Jon Snow. When Rhaegar is killed, does this mean Jon is next in line to the throne? Is Jon the rightful king?
Or, does Targaryeon succession go indiscriminately to male and female siblings? I don't think so, because Westeros has not had a Targaryeon Queen. But, under that scenario, older brother Rhaegar dies (killed at Battle of Trident) and so King Aerys II's other children become heirs -- Viserys first, and when he dies, then Daenerys.
Is Daenerys the rightful ruler? Or does Jon Snow have a more legitimate claim to the throne, through his parentage by Rhaegar?
Probably doesn't matter because it seems inevitable that they will marry and unite Ice and Fire.
Well, if there was an annulment of Rhaegar's marriage to Elia Martell, and he subsequently married Lyanna Stark, then I would think that Jon Snow would be the legitimate heir to the Iron Throne. Now, two weeks ago, I would have said no to that proposition, because, as far as I knew, Lyanna & Rhaegar were not married. But, if they were legally married, he having gotten rid of his first wife, then I think Jon does have a claim to the throne.
Bigger question: Would Jon want the Iron Throne?
The Targaryans fought several civil wars over the succession. At the time of the show, the Blackfyre rebellions (a family quarrel over the succession) were a fairly fresh memory. Barristan Selmy and others of their generation cut their teeth in the fourth Blackfyre war. Brynden Rivers, who viewers know as the Three Eyed Raven in the show, was a major figure in all four Blackfyre wars before being sent to the Wall, becoming Lord Commander of the Night's Watch, and disappearing on a ranging expedition. Prior to his exile, he was regarded as a powerful sorcerer, and much feared; he presumably was a greenseer and a warg. No one in Westeros knew what became of him until Bran reached him, and it is not clear that Bran has made the connection. (The books do not tell if Maester Aemon knew the Three Eyed Raven's identity; that would be an interesting question as he and Rivers were contemporaries, close relatives, and joined the Night's Watch at the same time.) The Blackfyre exiles, organized as a mercenary company, play an important role in the books but have been written out of the show.
Anyhow, the Targaryan line of succession was as improvisational as everything else in Westeros. If Jon and Dany fight over the succession, there is ample precedent.
Jon has the strongest claim if he can PROVE that the marriage took place AND that he’s the resulting child.
Then it becomes a matter of who is willing to back him.
If he marries Daenerys to create peace and takes the throne with her, then it is a union of ice and fire.
What would be interesting is if they make Sansa and Tyrion’s children heirs to the throne, since Daenrys cannot have children. The hand of the king has a vested interest in running the realm, Sansa is still the mother of princes and princesses both for the realm and the North. And likely Casterly Rock, too.