We do not know.
Even though the story we follow has many of the POV characters in attendence at the Tourney at Harrenhal, none of them seemed to notice Elia's reaction to Lyanna being crowned the Queen of Love and Beauty. Although, it was known by all in attenedance that this was not a good omen.
Ned remembered the moment when all the smiles died, when Prince Rhaegar Targaryen urged his horse past his own wife, the Dornish princess Elia Martell, to lay the queen of beauty's laurel in Lyanna's lap. He could see it still: a crown of winter roses, blue as frost.
Thoughts of Ned Stark - A Game of Thrones, Eddard XV
We do know that Rhaegar was obsessed with the prophecy of the Prince that was Promised, beliving the prince would be one of his own children (specifically his first born son Aegon) and that "there must be one more, the dragon has three heads". We also know that Elia nearly died from birthing Aegon and was told that she could not bear any more children.
George describes the relationship as complex.
"But that was the tourney when he crowned Lyanna Stark as queen of love and beauty!" said Dany. "Princess Elia was there, his wife, and yet my brother gave the crown to the Stark girl, and later stole her away from her betrothed. How could he do that? Did the Dornish woman treat him so ill?"
"It is not for such as me to say what might have been in your brother's heart, Your Grace. The Princess Elia was a good and gracious lady, though her health was ever delicate."
Barristan Selmy to Daenerys Targaryen, A Storm of Swords - Daenerys IV