The dilemma in "The Drunkard" is how to keep Mick Delaney from getting drunk at the public house following the funeral of his friend and confidante Mr. Dooley. Frank O'Connor structures the story so that an extremely emotional and compelling event virtually inescapably drives Mick, who has a problem with drunkenness, to the public house. The thought of Mick in the public house and the inevitable consequences for Mick distress his wife to the extreme causing her to reach for extreme measures to fend off the inevitable.
So in hopes of resolving the dilemma of Mick needing to be at his friend's funeral followed up by an emotional stop at the public house, she sends their son with him to try to help him keep the "brakes" on his drinking. The catastrophe, of course, is that Larry becomes drunk himself. The theme is the irresponsibility and horrendous of the habitual drunkard, whether the drunkard him/herself or a boy imitating the drunkard.