Not sure why Rhaegar needed an annulment. Targs have been polygamous before, though none have been since Maegor the Cruel. Even Aegon the conqueror had two wives.
It also possibly renders his older two kids illegitimate. Part of the reason he hooked up with Lyanna was his obsession with a dragon having three heads and after having her second child Elia Martell was told a third would kill her.
Dumping a faithful loving wife seems cruel personally and stupid in that it alienates Dorne in the middle of a giant civil war....Dorne was already pissed he ran off with another woman and only reluctantly sent 10,000 men.
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"A man without a belly is like a house without a balcony"
- Old Turkish saying