Miranda even says, "My father's of a better nature, sir,/Than he appears by speech" (I.ii.500-501). Shakespeare may have been writing Prospero like this only to juxtapose his warm nature at the end of the play, which gives the play a "and they lived happily ever after" feel.
Prospero uses his magic to control the spirit Ariel, which gives him a lot of power. Prospero knows of Caliban, Stephano, and Trinculos' plot to kill the king and he uses this knowledge to his own advantage. He thinks that when he takes back his throne in Milan, he can use it as blackmail against them. He thinks that they will do whatever he says because of this and because of the fact that Miranda will become queen one day.
Prospero shows his protective side as a father to Miranda. He tries to make sure that Ferdinand really loves Miranda by making her seem more difficult to get. He is worried that their love won't last and he doesn't want this for her. He wants to make sure that Ferdinand knows the greatness he is getting in the love of Miranda, which makes Prospero seem downright sweet, even if his language comes across as scheming and vindictive. It is very clear that he loves his daughter and wants only what is best for her.
By the end of the story, Prospero is able to forgive Antonio and Caliban, which shows how he has changed as a man. After Caliban has forced himself upon Miranda and has actually tried to kill Prospero himself, Prospero is able to find forgiveness for him. Prospero is even able to forgive his brother for taking his position in Milan and casting him and his daughter out to sea. It is precisely because of this change in Prospero from a vengeful, scheming man to a protective and forgiving man that he is able to get off the island. It is rather symbolic if we look at the island as a representation of power and Prospero's obsession with power. It was what kept him at a distance from his true nature and from his real self. Once Prospero was able to let that side of his personality go and let the true, loving nature come forth, he is able to get off the island.
Prospero forgives the people who have hurt him most and his letting go of Ariel, freeing him, is symbolic of him letting that need for power go. "The rarer action is/in virtue than in vengeance" (V., i., 27-28). Prospero can go back to Milan and be the Duke that he should have been -- only this time he will be better because he is a different person. He is now happy and not spiteful; he is now loving and not in need of controlling others for his own gain.
It is apparent throughout the play that Prospero is our hero. Behind all of his selfish acts of power, we can hear the true nature of the man. He has an innate sense of reason that always keep us believing in him, despite all of the things he does and the control that he has over Ariel and Caliban and that which he wants to have over everything else. He is a man of cultivation and reason and this is why we always keep believing in him -- that he will change into the person he is destined to be, the person he really is. Shakespeare takes us on a journey to a far off land and introduces us to a character who is far away from his home both in person and in spirit. Through acts of magic and through acts of humanity, Prospero becomes the person that we have always believed him to be.
Our revels now are ended. These our actors,
As I foretold you, were all spirits, and Are melted into air, into thin air:
And, like the baseless fabric of this vision,
The cloud-capped towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep (IV.i., 148-158).
Shakespeare, William. The Tempest (the Annotated Shakespeare). Yale University