Hal's internal struggle is illustrated in II.ii. This scene marks our first view of Hal in Henry IV, Part 2 (he was the central character of Henry IV, Part 1). He already seems a changed person, in the process of retreating from his previous life. However, although the hell-raising of his youth no longer appeals to the maturing prince, he does not yet seem quite ready to abandon his old friends; thus, we see Hal hanging out with Poins even as he says to him, "What a disgrace is it to me to remember thy name!" (12-13).
Hal's identity confusion is well demonstrated by his piteous question, "Doth it not show vilely in me to desire small beer?" (5-6). Most of us would not suffer so much anguish over wanting a mug of beer ("small beer," by the way, was a thinned-out version, often used for hangovers--and, thus, perhaps, a decent cure for Hal's weariness). In his struggle to define himself, however, and to put his past behind him, Hal seems to perceive this simple desire as a personal weakness.
Hal's character development, here and later on, owes a great deal to the events of Henry IV, Part 1. There are three important things to know about that earlier play: First, in it, we see Hal taking part in the life of the tavern with Falstaff and his friends, to the enormous disappointment of his father and the court nobles. Second, Hal tells the audience that this is actually all part of a plan--he is trying to make himself look like a hopeless bum so that everyone will be very impressed when he suddenly reforms himself into a king, (Henry IV, Part 1, I.ii). Third, in the middle of that play, Hal makes a solemn promise to his father that he will reform and act like a true prince from now on (III.ii). In the current scene (Henry IV, Part 2, II.ii), Hal is clearly pondering this promise and trying to figure out what is the right thing to do next--and whether or not that is what he actually wants to do.
Hal's sudden decision to spy on Falstaff in the Boar's Head Tavern is a little unexpected, given his solemnity and his father's sickness. We might read it as an attempt to distract himself from his concern about King Henry's worsening health; or, perhaps, as a result of his conflicting desires to abandon his friends and to remain with them.