I've had this idea for a while now, but I'm having trouble getting it to work, so I've decided to post it as a challenge instead with a rough outline of what I've been able to think of so far.

Proposed Title: Jaehaerys III

Summary: instead of a girl – canon Daenerys – Queen Rhaella's final child is a boy, whom she names Jaehaerys. Jaehaerys escapes with Viserys and grows up in Essos, and after his death decides to continue the struggle to reclaim his family's birthright.

Overview: Jaehaerys grows up meek and timid because of Viserys' attitude, and spends his time practicing archery and horseback riding as well as studying and therefore staying out of his brother's way. Viserys eventually marries a Dothraki princess in an effort to gain their support, but as in canon they ride east instead of west. Dragon eggs are presented as a wedding gift to Viserys by Jorah Mormont, who during their eastern travels takes Jaehaerys under his wing, helping him develop his self-esteem and how to use a sword. Jaehaerys eventually begins to join the Dothraki during their raids, earning their respect and Viserys' envy.

Eventually Viserys goes too far, and is killed. Fearing they will be next, Jorah and Jaehaerys steal the eggs and flee south, and despite a few encounters with Dothraki scouts make it to Qohor. They attempt to enlist the aid of the warlocks in waking the dragon, only to be rebuffed and for the warlocks to try and steal the eggs. After a bloody fight in the inn they're staying, they decide to make for Slaver's Bay, but are still pursued by the warlocks. A warlock manages to corner them in Astapor, but they are saved by Ser Barristan who convinces Jaehaerys to return by sea to Pentos. There Magister Illyrio has assembled the Golden Company, which agrees to support Jaehaerys in exchange for lands of their own in the Crownlands.

Jaehaerys then sails for Dorne, and lands in Sunspear where he marries Princess Arianne Martell. Dorne raises its banners for Jaehaerys, who prepares to march north.

From there on, whoever takes this challenge is free to do as they would, but the above is basically a starting guide which can be followed and/or ignored as desired. Jaehaerys has to come out on top in the end though…not much point in the story otherwise.

With regards to dragons, feel free to wake them or not, but in the case of the former I suggest an assassination attempt by either the Tyrells or the Lannisters which involves trapping and burning Jaehaerys…only for him to survive unharmed (except for his clothes) and with three young dragons of his own.