Actually, Hal is not off fighting elsewhere, but is already a dissolute tavern-goer. From RII, Act 5, Scene 3:
HENRY BOLINGBROKE
Can no man tell me of my unthrifty son?
'Tis full three months since I did see him last;
If any plague hang over us, 'tis he.
I would to God, my lords, he might be found:
Inquire at London, 'mongst the taverns there,
For there, they say, he daily doth frequent,
With unrestrained loose companions,
Even such, they say, as stand in narrow lanes,
And beat our watch, and rob our passengers;
Which he, young wanton and effeminate boy,
Takes on the point of honour to support
So dissolute a crew.
This is important because it prepares us for the Hal we find in Henry IV. Not the robust son Henry can be proud of (at which the King remarks that Hotspur is more his son than Hal), but a thief and degenerate, and (in Hal's own words): "a devil haunts thee in the likeness of an old fat man; a tun of man is thy companion."