Rhaegar has not ended his marriage to Elia. Elia got pregnant with Aegon shortly after the Ashford tourney where Rhaegar met Lyanna. Elia nearly died of childbirth and told that she cannot have another child. Rhaegar needed 3 heads of the dragon, ie children, for the Prince that was Promised prophecy.
So Rhaegar "abducted" Lyanna who was on her way to the wedding of Brandon Stark and Catelyn Tully in Riverrun. Lyanna was moved to the Tower of Joy in Dorne (Elia is Dornish). Lyanna was originally betrothed to Robert Baratheon.
Brandon rode to King's Landing demanding to fight Prince Rhaegar, but him and his father (and their friends like the Arryn heir) were killed by Aerys. No one officially knew where Rhaegar was. The rebellion started, Ned Stark, Jon Arryn and Robert Baratheon called the banners. In the meantime Rhaegar and Lyanna were shagging in Dorne.
At one point Rhaegar decided to put in a brief appearance in Kings Landing. He took the 3 best Kingsguards with him to guard Lyanna. 3 other Kingsguard led the troops and the 16-year-old newbie Jamie Lannister was told by Rhaegar to protect Elia and her children. Mainly from Aerys.
In the end Robert Baratheon killed Rhaegar by the Trident. The Lannisters realised they have to make a choice. Tywin never responded to Aerys's begging letters, but turned up at King's Landing with his troops. Sacked the city. Elia was brutally raped and murdered by the Mountain. Children were brutally murdered by Lannister soldiers. Jamie killed Aerys to stop KL being blown up. Sat on thrine to see who claims it.
Ned left in a huff over the murder of the children to lift the siege of Storm's End. On the way he got word where Lyanna was. Ned kill Kingsguards. Baby Jon went to Winterfell and got there before Catelyn, now married to Ned, even got there. Not a happy new wife there.
Robert married Cersei to reward the Lannisters.