Lines 174-185 explain the irony in the statement that the irish "stay at home on purpose to deliver the kingdom to the pretender" ?

By these words, which are part of Johathan's Swift's "A Modest Proposal" (1729), the author is referring to the claim to the throne of England, Ireland and Scotland by James Francis Edward Stuart, son of King James II. The latter was a Catholic King, who had already fathered a daughter named Mary; until James Francis Edward's birth, Mary, who had been raised as a Protestant, was the legitimate heiress to the English throne. James Francis Edward was a Catholic. The English Protestants were reluctant to have a Catholic king, as they did not wish to be under the political influence of the Pope. Therefore, they rebelled against James II, whom they overthrew. Mary and her husband William of Orange then became Protestant Queen and King of England, Ireland and Scotland. Ireland is the "home" to which Swift refers in this statement. Since the Irish were and are Catholic, they wished to help James Francis Edward Stuart regain his position as heir to the British, Irish and Scottish crown. Swift contrasts these irish men with those Protestants who would rather leave England than pay taxes to a Catholic king.

James Francis Edward's attempts to regain the crown were unsuccessful.

it ends with a marriage, but also with prospero giving up his power.

the tempest is a play written by william shakespeare between 1610-1611, it narrates the story of prospero a magician that sets a storm to wreck a ship, this sets the story to kill the king of naples. while it is a romantic style play, it isn´t traditional because of the ending, it end with the marriage and the magician giving up his powers.