The whole annulment thing in the show is so dumb. In the middle of a civil war where Dorne is already pissed at the slight to Elia and is only grudgingly sending troops he makes it worse by annulling the marriage?
Targs in the past have had multiple wives (including Aegon the conqueror) though none had done so since Maegor the Cruel. Elia basically was not able to have children any more without risk to her life, so he could have got himself some sort of dispensation to get wife number 2 rather than throw the legitimacy of his children into question.
The thing that comes from the books is the other than Robert (for obvious reasons) EVERYBODY living loves Rahegar. Even Ned has no negative feelings in his POV, Cersei thinks of him as the one that got away, Barristan and Jamie both looked up to him. An annulment for a faithful wife would be something Henry VIII would do, not Rhaegar...just a deviation from where the character actually should be.
But then they did the same thing for Robb Stark (in having him get married because he is horny rather than a Ned Starkian sense of honor) in season 2, so why not Rhaegar.
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"A man without a belly is like a house without a balcony"
- Old Turkish saying