Prospero has been wrongly thrust onto this island, and that wrong must be addressed, or, by Jove, this isn't a play by William Shakespeare.
We find Prospero with a loving and precocious daughter, who has a sensitivity towards those she has not met (namely everybody). Prospero has two servants, and is well kept on the island.
We meet Prospero when he is anxious about the work he has ahead. His power depends on getting this timing right. Unlike a traditional frustration stage, we're not really worried that Prospero won't pull it all off (nor is he). Why? Because the play isn't really about the plot at all, since Prospero has already moved all of his enemies to the island in the first scene of the first act.
Again, not so much of a nightmare – we've seen that Prospero's power is amazing enough to create a tempest, and his manservant (or spirit servant) Ariel is fiercely competent. It is distressing though, to have two murder plots hatched simultaneously. Prospero must face and stop both of these attempts at treachery.
Beautiful magic is performed all around, and Prospero gets over his vengeance kick while the bad guys escape the punishment they deserve. This works for some of them, and all of this mercy and good feeling is an all-around new start for everyone – they return to their old land with freshly clean consciences and clear futures.