Anon, the truth is that we do not know the extent of what Rhaegar told Elia. How much she knew of his plans. We could argue back and forth all day; we would be merely speculating and having our own biased headcanons. However, let’s work with the canon material we have to build an argument.
ONE. By the way, the scene you mentioned is ambiguous in itself, because it happens to be a vision in the House of the Undying. Dany herself cannot be sure who Rhaegar was addressing.
"Will you make a song for him?" the woman asked.
"He has a song," the man replied. "He is the prince that was promised, and his is the song of ice and fire." He looked up when he said it and his eyes met Dany's, and it seemed as if he saw her standing there beyond the door. "There must be one more," he said, though whether he was speaking to her or the woman in the bed she could not say. "The dragon has three heads." He went to the window seat, picked up a harp, and ran his fingers lightly over its silvery strings. Sweet sadness filled the room as man and wife and babe faded like the morning mist, only the music lingering behind to speed her on her way. [Daenerys IV, ACOK]
Here, I even highlighted the passage for you. Not hard to understand we cannot take it at face value, right?
TWO. Rhaegar had plans to deal with his father. The only one who had a pacific way of deposing Aerys, actually, through a Council.
But if indeed there was a shadow, who was he, and why did he choose to keep his role a secret? A dozen names have been put forward over the years, but only one seems truly compelling: Rhaegar Targaryen, Prince of Dragonstone.
If this tale be believed, 'twas Prince Rhaegar who urged Lord Walter to hold the tourney, using his lordship's brother Ser Oswell as a gobetween. Rhaegar provided Whent with gold sufficient for splendid prizes in order to bring as many lords and knights to Harrenhal as possible. The prince, it is said, had no interest in the tourney as a tourney; his intent was to gather the great lords of the realm together in what amounted to an informal Great Council, in order to discuss ways and means of dealing with the madness of his father, King Aerys II, possibly by means of a regency or a forced abdication.
If indeed this was the purpose behind the tourney, it was a perilous game that Rhaegar Targaryen was playing. Though few doubted that Aerys had taken leave of his senses, many still had good reason to oppose his removal from the Iron Throne, for certain courtiers and councillors had gained great wealth and power through the king's caprice and knew that they stood to lose all should Prince Rhaegar come to power. [The Fall of the Dragons: The Year of the False Spring, TWOIAF]
This claim is supported by Rhaegar’s own words, in a conversation with Jaime.
Rhaegar had put his hand on Jaime's shoulder. "When this battle's done I mean to call a council. Changes will be made. I meant to do it long ago, but . . . well, it does no good to speak of roads not taken. We shall talk when I return."
Those were the last words Rhaegar Targaryen ever spoke to him. Outside the gates an army had assembled, whilst another descended on the Trident. So the Prince of Dragonstone mounted up and donned his tall black helm, and rode forth to his doom. [Jaime I, AFFC]
So you cannot claim that Rhaegar was not aware of Aerys II’s inaptitude to sit the Iron Throne and did not mean to do something. However, there are three issues regarding Aerys II: 1. TWOIF remarks he had his own supporters, men that hated Rhaegar and wanted him passed in favor of Viserys; 2. he was still the king; and 3. he was still Rhaegar’s father. Rhaegar could not commit treason, nor kinslaying or kingslaying. Those are all taboos in Westerosi society. It was not as easy as we would like to depose a king, who would have imagined, right?
THREE. Rhaegar did not crown Lyanna with the intent of humiliating Elia, as you put it. It is speculated to be a move to curry favor with the lords attending the tourney, especially the Starks and the Baratheons, for his political purpose of deposing Aerys II.
The cheers of the crowd were said to be deafening, but King Aerys did not join them. Far from being proud and pleased by his heir's skill at arms, His Grace saw it as a threat. Lords Chelsted and Staunton inflamed his suspicions further, declaring that Prince Rhaegar had entered the lists to curry favor with the commons and remind the assembled lords that he was a puissant warrior, a true heir to Aegon the Conqueror. [The Fall of the Dragons: The Year of the False Spring, TWOIAF]
And when the triumphant Prince of Dragonstone named Lyanna Stark, daughter of the Lord of Winterfell, the queen of love and beauty, placing a garland of blue roses in her lap with the tip of his lance, the lickspittle lords gathered around the king declared that further proof of his perfidy. Why would the prince have thus given insult to his own wife, the Princess Elia Martell of Dorne (who was present), unless it was to help him gain the Iron Throne? The crowning of the Stark girl, who was by all reports a wild and boyish young thing with none of the Princess Elia's delicate beauty, could only have been meant to win the allegiance of Winterfell to Prince Rhaegar's cause, Symond Staunton suggested to the king.
Yet if this were true, why did Lady Lyanna's brothers seem so distraught at the honor the prince had bestowed upon her? Brandon Stark, the heir to Winterfell, had to be restrained from confronting Rhaegar at what he took as a slight upon his sister's honor, for Lyanna Stark had long been betrothed to Robert Baratheon, Lord of Storm's End. Eddard Stark, Brandon's younger brother and a close friend to Lord Robert, was calmer but no more pleased. As for Robert Baratheon himself, some say he laughed at the prince's gesture, claiming that Rhaegar had done no more than pay Lyanna her due...but those who knew him better say the young lord brooded on the insult, and that his heart hardened toward the Prince of Dragonstone from that day forth. [The Fall of the Dragons: The Year of the False Spring, TWOIAF]
Well, here we have hints of Rhaegar participation in the jousts and his posterior crowning of Lyanna as a political move (as well as to honor her for The Knight of the Laughing Three). Did it go wrong? Of course! The Starks and Robert were distraught and not too pleased. Rhaegar tried, nevertheless. He thought his gallantry would earn him support for his cause (in comparison to Aerys II’s appearance and overall behavior, mind you).
As you might have noticed, we can understand a little more of Rhaegar’s reasons, but not Elia’s perspective on the whole ordeal. However, if she was aware of what he wanted to achieve at Harrenhal, it is safe to conclude a sensible woman such as Elia would not begrudge him for making a move. Again, we cannot be sure about her, because GRRM did not bother to give us Elia’s perspective. It does not even matter, frankly.
FOUR. The circumstance of Rhaegar and Elia’s relationship was this: a political match made by the Princess of Dorne; borne out of duty, not out of love. However, there was good feelings between them, even if it was not love. Whether she was aware or Rhaegar’s feelings for Lyanna or not, I cannot say. But nothing about her (arranged) marriage, personality and upbringing suggest that she would have raged or hated Rhaegar and Lyanna’s guts because he took a mistress he loved. We have to remember she was a Dornish noblewoman, born and raised in a faux-medieval society. Alliances by marriage were the order; and people had lovers they desired and loved. Her context differs much from ours.
FIVE. The Rebellion (and thus the deaths of thousand of dornishmen) did not start because Rhaegar and Lyanna eloped. It started because of Brandon’s impulsiveness and lack of tactic (shouting for the death of the Crown Prince is a treason, a huge crime paid with death), and because Aerys II not only murdered Rickard Stark, but demanded the heads of Ned and Robert as well. Then Jon Arryn raised his banners in war. It was a situation that got out of control.
SIX. Why are you talking babies? It quite does not have anything to do with the situation at hand. Elia was not put in a situation in which she had to make such a choice for her son’s life (unless you consider Young Griff to be the real Aegon).
SEVEN. Why do you think Jon would have risen in rebellion and comparing this situation to the Blackfyre’s Rebellions? Do you have anything to back up your claim? It seems you have a bias against bastards, quite frankly. And this is a mere hipotetical situation, because we know how the Rebellion ended.
EIGHT. At the end of the day, you seem to forget that, despite of Rhaegar’s relationship with Lyanna, Elia was still his legal wife. She was the mother of his heir, the next queen consort and the second in the line of succession to Dorne. Lyanna’s status highly differs from hers. Unless claimed otherwise on the next books, Lyanna was a lover (a mistress, if you would), with no legal marital status. Again, unless claimed otherwise, Jon would still be a bastard. Even if Rhaegar legitimized Jon to give him the Targaryen name, he would still be the second son, under Aegon in the line of succession. I do not see any lord going against that or tempted to usurp Aegon. Even more so that Aegon had the Targaryen look, whilst Jon does not. I quite doubt a lord would rise in rebellion to supplant the heir ir favor of a Northern-looking boy, in those circumstances.
Actually, Viserys was the one to be feared here, not Jon. Because Aerys II’s supports wanted to take Rhaegar and his children out of the line of succession, fearing they would lose power and wealth.
Tell me the truth now. Who would have Elia feared: her son’s legitimate and Targaryen-looking uncle or Rhaegar’s Northern-looking baseborn son? I think the answer is obvious.