Prospero, a mage and former Duke of Milan, and his daughter Miranda have been stranded for 12 years on an island. Prospero's brother Antonio, who deposed him, is shipwrecked with his son Ferdinand. By the end Ferdinand and Miranda are married and Prospero, after abjuring magic, regains his title and forgives his betrayers.
The description is incorrect- Ferdinand is the son of Alonso, the King of Naples, who worked with Prospero’s brother, Antonio, to dethrone him of his dukedom. Antonio’s son is a very minor and barely mentioned character.