The reason is because of the whole Trial by Combat in which the Mountain kills Oberyn, who was her lover, and she has been bitter ever since. And that is not all. Oberyn was upset at the Lannisters because he believes that Tywin ordered his sister's rape and death (by the Mountain). So Ellaria will have continued his hatred for the Lannister family. And besides all of this, she is still very bitter about the Lannisters and Westertos because of the death of Oberyn and wanted the King of Dorne to declare war because of his death.