Prophecy vs Politics, Fantasy vs Reality
Given The Mad King causing a surge of interest in Rhaegar, Lyanna, and Elia, I want to offer that the tragedy of TPTWP foreshadows Dany's crossroads in Westeros.
"Will you make a song for him?" the woman asked.
"He has a song," the man replied. "He is the prince that was promised, and his is the song of ice and fire." He looked up when he said it and his eyes met Dany's, and it seemed as if he saw her standing there beyond the door. "There must be one more," he said, though whether he was speaking to her or the woman in the bed she could not say. "The dragon has three heads."
We can look at the end of Rhaegar's life as a conflict between his desire to pursue prophecy (the Song of Ice and Fire) and the political reality that he needed to organize the nobility to help him depose his mentally unstable father. This is made explicit by the play, but is clear in the books as well. Rhaegar sponsors the tourney at Harrenhal to rally support, but then he ends up getting distracted with the Knight of the Laughing Tree (Lyanna).
Rhaegar is torn between fantasy and reality:
- Lyanna represents prophecy / fantasy
- Elia represents politics / reality.
Dany's story is headed for the same crossroads:
- Jon (son of Lyanna) represents prophecy / fantasy.
- Aegon (alleged son of Elia) represents politics / reality.
The purpose of there being two hidden sons of Rhaegar in the Dany story is to show the crossroads. Jon exists for the song of ice and fire. Aegon exists for the Iron Throne. As with Rhaegar, the conflict comes from trying to have both.
The Tragedy waiting at Storm's End
The tragedy of Rhaegar Targaryen is that he has to leave the waking dream that is the Tower of Joy and face the crushing reality of Robert's war hammer. The play makes this overly literal by having him distracted by a dragon dream in the middle of the battle, but the actual thematic point is that Rhaegar is killed for pursuing his dreams.
"I see them in my dreams, Sam. I see a red star bleeding in the sky. I still remember red. I see their shadows on the snow, hear the crack of leathern wings, feel their hot breath. My brothers dreamed of dragons too, and the dreams killed them, every one*. Sam, we tremble on the cusp of half-remembered prophecies, of wonders and terrors that no man now living could hope to comprehend . . . or . . ."*
"Or?" said Sam.
". . . or not." Aemon chuckled softly. "Or I am an old man, feverish and dying."
In Westeros Dany faces the same conflict. Either fly into the wonders and terrors of prophecy that no man living could hope to comprehend . . . or not.
That night she dreamt that she was Rhaegar, riding to the Trident. But she was mounted on a dragon, not a horse. When she saw the Usurper's rebel host across the river they were armored all in ice, but she bathed them in dragonfire and they melted away like dew and turned the Trident into a torrent. Some small part of her knew that she was dreaming, but another part exulted. This is how it was meant to be. The other was a nightmare, and I have only now awakened. ~ Daenerys III, ASOS
Even if Danerys Stormborn succeeds in finding the third head of the dragon and playing out the Song of Ice and Fire, we must eventually awaken from that fantasy and face the complicated reality waiting for her at Storm's End.
tldr; Rhaegar : (Lyanna, Elia) :: Daenerys : (Jon, Aegon)