In Shakespeare's Hamlet, what is ironic about Claudius' pleasure when he learns that Hamlet wants Claudius to watch the play?
The irony here is based upon the fact that Hamlet is using the play to pin Claudius for the murder of Hamlet's father. First, it would be pertinent to reveal the lines referred to here:
Polonius. 'Tis most true, / And he beseeched me to entreat your Majesties / To hear and see the matter.
King. With all my heart, and it doth much content me / To hear him so inclined. / Good gentlemen, give him a further edge / And drive his purpose into these delights. (3.1.22-27)
Hamlet has actually persuaded the players to do this particular play (The Murder of Gonzago) which reveals a murder achieved in order to gain the love of the victim's wife. The entire reason behind this is to corner Claudius into revealing his guilt. So, of course he has entreated Claudius and Gertrude "to see and hear the matter." As usual, Hamlet is using Polonius as the fool of the play. It is significant to note, however, the reason why Claudius is so content with the idea of watching this play. The reason is that Claudius, Gertrude, Polonius, and others have been trying to figure out the reasoning behind Hamlet's "distraction" to no avail, so far. They have an inkling that Hamlet's change in mental capacity has something to do with Ophelia, but they are not sure. (In reality, of course, Hamlet has chosen to put "an antic disposition on" in order to fool everyone.) Furthermore, Claudius & Friends are planning to sit Hamlet right next to Ophelia and watch him like a hawk. That is why Claudius is so excited and why he asks to "drive his purpose into these delights."