I do not own Game of Thrones
Naturally being in Dorne which was fighting for him made it the ideal kingdom to lead from for Rhaegar. He joined Prince Doran and Prince Oberyn who had returned, but he underestimated their boundless malice. Breaking guest rights was something they had already done before. The Martell brothers considered killing him for the insult he did to their sister but they didn't want her to become a widow. Instead they started giving him a poison that would not harm his health but his seed and eventually turn him impotent. Elia couldn't have anymore children anyway and they didn't want to risk him having children with Lyanna or Cersei.
On a first glace crown seemed to be in a stronger position, specially with the humongous army of the Reach. In reality though, Westerlands were the only monolithic kingdom because of Tywin's fear. All Kingdoms had a second place family wanting to displace their lord paramount except Tywin who had crushed them. Riverlands and Reach were far too split. House Royce of Vale were first men and hence mostly opposed to Arryns though it wasn't as bad at that time. Jon Connington was obsessively loyal to Rhaegar and so stood apposed to the Baratheons. Dorne had Yronwoods antagonistic to the Martells thanks to Oberyn's antics.
Jon Connington confronted Stannis before the Stormland banners could assemble slowing them down. Florents did the same to Mace Tyrell. This allowed Dorne led by Rhaegar to swiftly bypass them unhindered. Jon Arryn had to be careful while assembling the knights of Vale and descending from mountains due to the mountain clans. The delay allowed Tywin to crush the lords of Riverlands who were with Aerys like Brackens and united them under Hoster Tully. He left them to face the Vale and marched his army down to Kings Landing quickly.
Naturally Aerys did not open the gates for them, but swaying the city watch with bribes was not hard. Unfortunately Dorne joined them by that time. Being on the same side did not make them friends. Doran knew that Tywin wanted Rhaegar to marry Cersei and most likely was also targeting Elia's children. It was a miracle that his son Jaime had acted on his own to bring Elia back to them.
Both armies got into a race about who could sack the city faster. Rhaegar attempted to keep things civil, did not work when blood of all men was boiling. Killing and raping was a common scenery by the time they reached the Red Keep. Surprisingly Aerys looked calm and completely sane while sitting on the Iron Throne, like he was before the 'war of nine-penny kings'. He welcomed them all with a smile.
"Welcome back my prodigal son. I see that you've brought the in-laws. Also my old friend." Aerys spoke in a jovial tone more suited to a Manderly.
Rhaegar hesitated for a bit in shock but recovered soon.
"Father. The throne has wounded you enough. Please step down and let me carry this burden from now on."
"You know. I was thinking the exact opposite thing. Its a fathers and kings job to delay his successors from sitting on this uncomfortable chair for as long as possible."
"If your mental state had not deteriorated to this degree. I hesitated for so long to avoid becoming kinslayer."
"That is very upright of you son. It would mean something too if only you hadn't run off with the northern bitch. Tell me. Do I look mad to you now?"
This was indeed something that was bothering not only Rhaegar, but Tywin, Doran and Oberyn as well. Why did his sanity suddenly return? Specially Tywin realized that the resistance by the city watch and Crownland's volunteers was far too weak.
"What are you buying time for? Is there a sellsword company scheduled to arrive and save you?"
Aerys turned to Tywin and became somber.
"I wanted to apologize to you, my friend. Its true that I loved Joanna, but she would likely hate me for how I have treated you. We'll both see her in afterlife. Steffon would have never let our friendship get ruined to this degree."
Tywin was also shocked at this heartfelt display of emotion. Aerys turned to the Dornish princes.
"You people have been a thorn to my family forever. Haah. Unbowed. Unbent. Unbroken. I can even respect the sacrifices you made to kill Rhaenys and her dragon. But you broke guest rights to kill the young dragon and we rewarded you for it by royal titles when you joined us. Its because of people like you that I have trust issues. Both your men and women are nothing but whores. Your deaths are something I will regret even less than my frenemy over here."
Oberyn was shaking in anger but Doran realized that they had made a terrible mistake.
"Quick. Order a retreat..."
"Its too late. Hahahaha... My son, lets see if fire indeed cannot burn a dragon."
Explosions rocked the entire capital and soon the whole city of Kings Landing along with all of its keeps, half-a-million people, 60,000 Westerland soldiers and 45,000 Dornish soldiers were all engulfed in a grave of green flames.