The Prince and the Pirate

There's a prince, in a fantasy kingdom, who has just turned fourteen. He's a man now, and his father sends him away to sea, the third brother to go. He has six older brothers, and will never be king, but he hopes to be high up in the navy someday. He learns a lot about sailing, but nobody will talk to him as a friend.
He returns home after three years at sea. His father has a quarrel with a priest, and plans to send the prince into the Temple of (A God) as a priest, to make up for this. The prince, horrified at the prospect of a life of celibacy and prayer, runs away. The king, embarrassed, sends his younger sister instead.
The prince decides to return to the sea, but looking like a wanderer can only find employment as a cabin boy. The other boys are younger than him, but he is short. He takes up a false name and grows out his hair, and is not recognised. The merchant ship he is travelling on is captured by pirates, who are quick to recognise his potential. He is 'forced' to become a pirate, and navigates for them.
The captain is a brave and foolish woman, with a magnetic personality. He is with the pirates for several weeks, when they capture a magnificent treasure galleon. They divide the treasure and retire wealthy men. The prince tells the captain that he wants adventure, and the captain agrees. With a like-minded crew, they set off in search of new lands.
The prince makes good friends with the ship's cook. The ship sails for many months, and rations are running low. They are growing desperate, when they finally spot land. They reach a shore, and disembark. It is a plentiful land, and they plan to colonise it. They walk for a week in both directions, and never meet - the land is vast.
They walk through the land, which is apparently deserted. They build a village on a hill, and find an edible plant. The prince reveals great knowledge of science, which comes in very useful. The captain suggests that, after a village is ready, they should return with the ship to find settlers.
The prince and the captain go together to look for humans, after they find a broken clay pot floating in the river. They are caught in a hunter's trap, and he takes them to see the chief. The new society that they find is more advanced than their own, and the prince takes a keen interest in their scientific knowledge.
The captain does something badass and saves the natives from some disaster, finding diamonds in the process. They return home in ships built by the natives (who have explored the archipelago which lies to the east of their island). The prince returns to a troubled land - shadows of war hover over his father's kingdom. He someohow fixes it, shouts at his dad, and gets rid of the stupid old religion. Democracy happens, spearheaded by the combination of the Pirate Code and the ways of the people across the sea.
The prince and the pirate captain get together, and retire off the wealth from the diamonds they found. Happy ending ensues.