When Prospero and Miranda landed on this island, and while he used his books to master its magic forces, he encountered two beings. Ariel was a spirit imprisoned by the now dead witch Sycorax; Prospero freed Ariel on condition that Ariel would serve him for a time. The other being was Caliban, the animalistic son of that same witch. Prospero at first befriended him. Caliban taught him what he knew about the island, and Prospero schooled Caliban in basic European or “civilized” knowledge, hoping to humanize him. But Caliban attempted to rape Miranda (an act he does not deny—it was, after all, his only opportunity to sire children.) Then everything changed, and the enraged Prospero used his powers to torment and enslave Caliban.
Beyond his rage, Prospero must have seen what this meant. His daughter was becoming a young woman (15 or 16 at the time of the play), while he was becoming an old man (now 50.) His powers would inevitably wane, until he could no longer protect her from Caliban. Eventually she would be alone on this island. What could he do?
The ship returning to Italy from Tunis in Africa was an opportunity he could seize upon. Evidently he knew exactly who was on board—not only his brother and the King of Naples, but the young Prince of Naples, a suitable husband for Miranda. He could bring the young people together to see if they were really a match. He could also magically confront the others with their offenses against him, and put himself in position to reclaim his dukedom and return to Milan, where he could take whatever further measures he could to secure Miranda’s future.
Prospero had to make sure Miranda would become a princess, and not a fling. That Prospero is conscious of his own impending death is expressed most beautifully in his “we are such stuff as dreams are made of" speech, but he also notes later than when he returns to Italy his every third thought will be of death. Even his final speech, when he begs for indulgence and prayers, it is because without his magic powers he is weak.
Commentators argue whether Prospero was intent on revenge or not, when he created the storm. Some vengeance, or at least accounting, was probably part of it, and he certainly still harbored anger. But he took care that the shipwreck didn’t kill or injure anyone. He did inflict torments on the ignoble Italian nobles, and was jolted out of his distracted cruelty by Ariel, but he had this goal beyond revenge--he could turn his justifiable revenge into forgiveness that actually doesn't seem all that sincere, but it is politically very smart. Especially if his goal is to secure Miranda's future.
The King of Naples thought his son was dead, but Prospero returned him alive, and with a wife. The grateful king became Prospero’s ally on the spot. Then Prospero let his brother know that he also knew of his conspiracy against the King of Naples hatched on the island, but would hold that knowledge in reserve. When he then boldly proclaimed he would take back his dukedom, his brother could hardly object.
|John Gielgud as Prospero (1951)|
These were deft and very effective political moves, meant to get him back to Italy where he could serve his daughter’s interests. For clearly he wasn’t much interested in returning for himself. Here on the island he had magic power, derived in part from his lifelong study. Now he had to give up his power (the staff) and his knowledge (his book), for a life of decline.
It's true that in plays of this era concerning royals, the health of relationships reflect on the health of the state: a good marriage suggests a goodly kingdom. There's some expression of this in the content of Prospero's magic show for Miranda and Ferdinand (which would have been done as a masque), when the goddess Ceres blesses the impending marriage, equating a fruitful royal couple with a fruitful land.
Yet I can't convince myself that Prospero cares very much about Milan except for his daughter's sake. He wants the marriage to be honorable, perhaps so that there's no taint of a child conceived out of wedlock that might affect the royal succession of his grandchildren. But more urgently it seems to be because he wants Miranda to have a stable, prosperous and fulfilled life.
|Mariah Gale and Patrick Stewart (2006-7)|
Granted all the other elements of the play, it is basically about a father—a single parent—seizing the opportunity to secure his daughter’s happiness and her future. One consequence of seeing the play this way is that it establishes Prospero as the protagonist—the one who is most active and propels the action. This may seem obvious, but many productions over the years have tended to emphasize other characters: Caliban (as a victim of colonialism and racism), Ariel (relationship to natural forces) or even Miranda.