The idea that Prince Rhaegar Targaryen was anything more than another supporter of the violent, malicious, and unholy rule of the Targaryen dynasty is a seditious lie.

His Grace, Robert of the House Baratheon would not have went to war over rumor or speculation. He knew it for a fact to be true that Prince Rhaegar kidnapped and subsequently violated Lyanna Stark. This alone is a deep blow to Prince Rhaegar's so-called morality.

If Prince Rhaegar had indeed planned to call a Great Council (of which there is a precedent, that much is fact.) he did not inform anyone of his intentions. When Robert Baratheon, Jon Arryn, and Eddard Stark called their banners and subsequently entered into a state of open rebellion against the Iron Throne, Prince Rhaegar made no attempt to make peace terms with the Rebellion, or in any way attempt to reach out to its leaders (or any other Lords in the land, for that matter.) and simply agreed to do as his father had commanded and lead the Crown's armies against the Rebels.

Had Prince Rhaegar attempted to aid the Rebellion in any way, or even pleaded with his father to abdicate the Throne, this question might have more merit. As the events of the Rebellion stand, however, there is no more evidence to suggest Prince Rhaegar had any intentions of deposing his father than there are the rumors that our benevolent ruler, Tommen of the House Baratheon, is a bastard born of incest, and indeed, both are nothing short of treasonous lies.

Found accounts from anonymous Lords that attended the tournament of Harrenhal state that the intentions of the conspiring Lords was to encourage or possibly even force Prince Rhaegar Targaryen to call a Great Council to begin drafting a binding document to institute limitations on the crown and to transition governing authority from the crown to a governing body made up of Lords chosen from amongst their own. This would have relegated the crown to little more than a figurehead in Westeros. Alas though, without an official account, we may never know.