-Daenerys and;ADWD Spoiler do not have any claim as the Targaryens lost their kingdom on a fair fight.Same works for Rhaegar,who,on my opinion,is alive,and hiding in Dorne as "The Darkstar".
To proove it:Their descriptions:
Rhaegar was exceedingly intelligent and excelled at anything he put his mind to, he was considered to be a talented musician and skilled knight. He was deeply affected by "the shadow of Summerhall", because he was "born in grief" and was considered melancholic at times.
Many think of Rhaegar with respect, even Robert's best friend, Ned Stark. Jaime still remembers the iron tones of Rhaegar’s voice.  Rhaegar was tall and handsome, he had dark lilac eyes and the silver hair of the Targaryens. His sister Daenerys Targaryen is often compared to Rhaegar as a compliment.
Gerold Dayne has an aquiline nose, high cheekbones and a strong jaw. He keeps his face clean-shaven. He has thick silver hair that falls to his collar like a silver glacier, divided by a streak of midnight black. His eyes appear black but at closer vantage they are a dark purple - dark and angry.
Arianne Martell thinks to herself that if there is a handsomer man in Dorne she does not know him. He has a cruel mouth and a crueler tongue. He is a cruel man. Arianne considers that if she were to take him as consort her father would question her good sense, but their children would be as beautiful as dragonlords.
That's an interesting idea, but wouldn't somebody recognize him? Considering his wife was Dornish, wouldn't many people in Dorne have known who he was if they met him?
A small complaint about the mod, shouldn't each of the Free Cities be controlled by its own individual faction, considering they are all independent cities?
No,if Doran Martell and Oberyn have arranged his hiding.Arianne and the Sand Snakes would be too young to recognise him and common dornishman couldn't have met him,because he might have never visited Dorne.Also,we have no record of Dornish Lords like Lord Yronwood,Qorgyle and so on to have had a meeting with Gerold Dayne.On the other side,Areo Hotah is blindly loyal to Doran and on his POVs we don't have many thoughts of his,he is more like an observer,so if he knew,GRRM would perfectly hide it from us.
are part of the plot.Varys had arranged the Dothraki and
invasions to eleminate all the anti-Targaryen resistence,as well
as he is killing all men capable enough to stop the invasion,i.e.Tywin Lannister(through Tyrion),Kevan Lannister and others that may perish in The Winds of Winter.
Let's hope Petyr Baelish,with the following titles:
Lord Paramount of the Trident
Lord of Harrenhal
Lord Regent of the Vale
Unofficial(you understand what I mean,the men with the following titles are in Baelish's control,so it's nearly the same as baelish had them):
Lord of the Eyrie
Defender of the Vale
Warden of the East
Warden of the South
Defender of the Marches
High Marshal of the Reach
Lord of Highgarden
will use the armies of the Riverlands,Vale and The Reach to stop them.