Hal is the Prince of Wales and heir to the British throne. He becomes King Henry V after his father, King Henry IV, dies in Act 5.
Before we think about Hal's character in Part 2, let's recap Hal's trajectory in Henry IV Part 1. In Part 1, Hal spent most of his time carousing with his low-life Eastcheap pals and taking every opportunity to thumb his nose at authority, which caused a huge rift between Hal and his father, King Henry IV. Henry IV worried about what would happen when Hal inherited the crown. Hal shocked the audience at the end of Act 1, Scene 2, when he delivered an infamous speech that was all about how his bad behavior was just a disguise or a role to be played. Hal said that he was pretending to be a degenerate in order to stage a dramatic "reformation" that would amaze his critics and make him a better king (Henry IV Part 1, 1.2.29). By the play's end, the prince redeemed himself on the battlefield by saving his father from the Scottish Douglas and by killing the rebel Hotspur. As a war hero, Hal shrugged off his bad-boy reputation and demonstrated his ability to govern. (You might want to read our in-depth "Character Analysis" of Prince Hal in our guide to Henry IV Part 1 to get some more information about the prince in his bad-boy days, but then come right back.)
The first thing we notice in Part 2 is that Hal doesn't appear on stage until Act 2, Scene 2 and even after that, we don't really see much of him at all. Given that Hal's our protagonist (and the guy who becomes king by the play's end) this is pretty striking. So, why do we see so little of Hal, anyway? The simple answer is that Hal spends most of his time laying low. Instead of carousing with wild friends and getting into trouble, Hal appears to be biding his time until he becomes king. Hal, then, seems to be a much more mature prince in Part 2.
Unfortunately, Hal also seems to be trapped in the "bad boy" role he created for himself in Part 1. This is made clear when Hal confides to Poins that, even though his "heart bleeds inwardly" because his father is sick, he can't show his grief in public because it would seem insincere, especially since he's spent most of his youth flipping his father the bird and being an all-around pain in the neck. So, even though Hal has matured, there's some evidence that most people don't know it yet.
Hal's relationship with his father, King Henry IV, is also on the rocks. Even though Hal saved his father's life at the end of Part 1, the prince is still hanging out with commoners like Ned Poins, which leads the king to believe that Hal hasn't changed a bit. In fact, Henry IV frequently complains that when he's dead and gone, the kingdom's going to fall apart with "riotous" Hal in charge (4.3.8). Warwick, however, seems to be the only character in the play who knows what's really going on. He defends the prince and tells King Henry IV what the audience has known all along: "The Prince will in the perfectness of time / Cast off his followers" (4.3.2).
Hal's tumultuous relationship with his father comes to a head when Prince Hal, thinking his father has died, takes the royal crown and tries it on for size. When the king wakes up from his little cat nap (whoops – turns out he's not dead after all!) the king is pretty ticked and goes off on his son, accusing Hal of hiding a "thousand daggers" in his "thoughts" (4.5.19). In other words, Henry IV has always suspected that Hal doesn't love him and wants to see him dead and the crown. (Apparently, Henry has forgotten all about how Hal saved his life during battle in Act T of Henry IV Part 1.)
The showdown between father and son makes for a pretty dramatic moment (it's the kind of scene reality television producers dream of) but it's also significant insofar as it speaks to the delicacy of lineal succession (when a direct descendent of the king, usually the king's eldest son, inherits the crown) and the consequences of primogeniture (the system by which eldest sons inherit their fathers' wealth, titles, lands, power, debt, etc.). In other words, Shakespeare is interested in exploring the idea that all sons (not just princes who stand to inherit kingdoms) inevitably look forward to their fathers' deaths. The "Henry" plays suggest (much like Hamlet and King Lear) that, in a society where lineal succession and primogeniture rule, as long as one's father is alive, a son has very limited power and wealth, which always has negative consequences for father-son relationships.
Of course, Prince Hal makes nice with his father just before King Henry IV dies but, the reconciliation between father and son hinges on Prince Hal's ability to convince his dad that his (Henry IV's) life is more important to him than the crown. Be sure to check out our discussion of "Quotes" for the theme of "Power" if you want to know more about this.
So, after Hal works things out with his sick father, all the daddy drama must be over, right? Nope. After Hal makes nice with his dad in Act 4, Scene 5 and then becomes King Henry V, he's got to contend with Falstaff, who was a kind of father figure to Prince Hal in Henry IV Part 1. When Falstaff travels to London to visit the newly crowned king in Part 2, Hal publicly rejects Falstaff, banishing the knight from his presence, which seems like a particularly cold thing to do to an old friend. So, what are we to make of this?
On the one hand, one could say that Hal (a.k.a. King Henry V) is a heartless jerk. OK, fine, that may be true, but there's much more at stake here. By publicly rejecting Falstaff, Hal completes his dramatic "reformation" by showing the world that he's no longer the bad-boy prince the world once thought he was. As King Henry V, Hal will be the man who will restore civil order to a nation that's been in turmoil. Hal may be a lousy friend, but he's a competent monarch, which seems, in this play, to be the more important quality.