If Rhaegar was already married (with children) to Princess Elia, how could he have eloped with Lyanna? I'm confused about this bit of the timeline and am wondering if Jon Snow isn't still a bastard after all?
The timeline is:
- Rhaegar weds Princess Elia Martell at some time before 280 AC.
- Princess Elia gives birth to two of his Children; Princess Rhaenys (born 280 AC) and Prince Aegon (born 281-282 AC). Maesters inform the Prince that Elia won't be able to bear any more children due to her poor health.
- Rhaegar tells Elia that Dragon must have three heads i.e. he must have one more child to fulfill an ancient prophecy. (Somewhere around Aegon's birth)
- Tourney of Harrenhal: Rhaegar and Lyanna meet each other. It is a possibility that they met after King Aerys ordered Prince Rhaegar to find the mysterious Knight of Laughing Tree because there is a very good theory that Knight of Laughing Tree was actually Lyanna in disguise. Rhaegar wins the Tourney and stuns the attendants by crowning Lyanna as Queen of love and beauty instead of his lady wife. This happened in 281 AC.
- "Abduction" of Lyanna: Next year the Starks travel to Riverrun for the marriage of Brandon Stark to Catelyn Tully. Rhaegar allegedly abducts Lyanna on the way. The year was 282 AC.
- Robert's Rebellion: Brandon goes to King's Landing to "kill" Prince Rhaegar. King Aerys killed both Brandon and his father Lord Rickard Stark. Rhaegar was not present. Then Aerys sends a command to Jon Arryn to kill his wards Robert Baratheon and Eddard Stark. Jon Arryn instead called his banners and thus Robert's Rebellion started. It began in 282 AC and continued till 283 AC.
There is nothing holding a married man from abducting another woman or taking a lover except morality. But it appears that Lyanna had indeed eloped with Rhaegar rather than getting married to Robert Baratheon. She was not happy with her betrothal to Robert because she feared that Robert would never restrain himself to one bed (So instead she ran away with a man who shared his bed with his legal wife, see how smart she was?).
We do not know about the marital status of Rhaegar and Lyanna yet. If someone is born out of wedlock, he is a bastard, regardless to who the parents are. Since Rhaegar and Lyanna are both Westerosi which is traditionally a monogamous region, it is less likely that Rhaegar and Lyanna married thus implying that Jon was born out of Wedlock.
However, There is the possibility that Rhaegar may have followed the precedent of two other Targaryens with multiple wives i.e. King Aegon the conqueror and King Maegor the cruel. If he did, Jon won't be a bastard since he was not born outside wedlock. But there is also a possibility that he may not have done that. So as of now, we do not know if Jon is indeed a bastard or not. Quoting GRRM:
[Questions concerning Targaryen polygamy.]
Maegor the Cruel has multiple wives, from lines outside his own, so there was and is precedent. However, the extent to which the Targaryen kings could defy convention, the Faith, and the opinions of the other lords decreased markedly after they no longer had dragons. If you have a dragon, you can have as many wives as you want, and people are less likely to object.
Also see, Will Jon still be a bastard?
UPDATE: In Season 7, it is revealed that Rhaegar had his marriage to Elia annulled and married someone else. That someone else can only be Lyanna, making Jon a legitimate Child. So it is all but confirmed in the show that Jon is now a trueborn Targaryen.
Gilly: What does "annulment" mean?
Sam: It's when a man sets aside his lawful wife.
Gilly: Maynard says here that he issued an annulment for a Prince "Ragger" and remarried him to someone else at the same time in a secret ceremony in Dorne. Is that a common thing in the south or--?