Just FYI - I voted on this topic and tried to hit the 5 star, but I moved the mouse at the wrong time and clicked on 3 stars. That was just a misvote on my part - I LOVE this topic! :)
I think Hamlet takes great delight in the scene with the "play within the play." He uses puns to goad the king:
Claudius: Have you heard the argument? Is there no offense in't?
Hamlet: No, no, they do but jest, poison in jest. No offense i'th' world.
Claudius: What do you call the play?
Hamlet: The Mousetrap....'Tis a knavish piece of work, but what of that? Your Majesty, and we that have free souls, it touches us not.
The use of puns shows that our character Hamlet is having a good time at the expense of the king and is enjoying watching Claudius squirm.
In addition, he is beside himself with glee when Claudius shows his hand and rushes from the room after calling for lights. Hamlet sings a snippet of a song about a wounded deer that runs off to weep and die, then double checks with Horatio about what he observed, saying he is convinced completely by what the ghost told him. Then Hamlet calls for more music and revelry!
This is not our usual gloomy Hamlet. He is thrilled to death that his mousetrap worked and is ready to celebrate!
I think that Hamlet really struggles with his feelings about his mission to murder Claudius. I don't really know that he's trying to "make a better mousetrap" as much as he's stalling because he afraid of actually committing a murder himself. He doesn't murder Claudius the first chance he gets because he thinks he's praying, but I really think he was making an excuse so he could buy more time before actually mustering the courage to do it. Then when he kills Polonius, thinking it was Claudius, by mistake we see a little glee there, although I think it's almost relief that he's finished the job. Then he's disappointed to spy Polonius beneath the arras and he feels that the rat deserved what he got for being so meddlesome. When he finally forces the king to drink I didn't feel like it was glee, I felt like he was making sure he finished what he started, but this wasn't how he imagined his revenge plot unfolding so I don't think there was any glee in snapping the final trap just relief for being able to die avenging his own father's death.