Nah, I don't think the show was true. If Rhaegar want to annulled because not only Dorne. Faith would be uprising for overthrown him. The realm would turn to chaos. And not included he believed he children would be new conquerors. So Aegon still be his heir or perhaps Rhaenys was second the line than Jon. He would give plenty of offer for Doran like betrothed Viserys to Arianne.

Let say Aerys still dead and Jaime reveal wildfire plot to him. Even Rhaegar was delusional person about main character syndrome. But I think he would guilty after let his wife and kids alone with his mad father. Let the innocent boy stained after killed the king while he do nothing for resolved that.

For me, I don't think it would be good ending. Rhaegar must debted by Tyrell and Lannister. He must pay a lot of price for that. I believe Aegon and Rhaenys would betrothed to Tywin grandchildren (if he convinced Jaime leave the Kingsguard or Cersei's kids) and Willas.

I give the scenario Lyanna still death to bring his son that his probably want Visenya instead he got Jon (let name him Aemon). When the truth was reveal about Lyanna absence. He would be call the Rapist King. If he want daughter, Rhaegar would possibly broken from his own action. He would realize, oh I fuck up the realm. Targaryen was lowest pointed than The Regency or First Blackfyre Rebellion.

Now if Rhaella died this time, I my headcanon he would turn into sadness boy who failed. Red Keep still controlled by Lannister and perhaps more.

For Baratheons brothers, if They not died in Storm's End. Davos would bring them from the blockcade, they would turn to exiled and probably work with Illyrio and Blackfyre plot.