The first stanza stanza makes it clear that the father is an alcoholic. The descriptiveness of the smell through the dizziness and having to hang on "like death" make the reader understand that the father has consumed a pretty hefty portion of alcohol. However, hanging on like death is the first place where we can question what the boy is thinking. He could be hanging on in fear. If he were to let go and get away, his father could just grab him even harder. Despite knowing he is about to receive some sort of punishment for his father, he fears that trying to escape could just make it even worse. On the other hand he could be clinging to his father in enjoyment. Despite the nearly unbearable smell, he refuses to let go as it would cause the fun to end. They bump into stuff, knocking things off shelves and making a lot of noise, causing an unfaltering frown from his mother. This frown is very easily tied to watching her alcoholic husband beat her child. While she clearly doesn't approve of her husband's actions, she may also fear him as the child does for he may drunkenly harm her also. However, whenever boys play and run around and knock things over, mother is always the first to disapprove. The father and child could very easily be play wrestling or something of the sort, and the mother is frustrated with the ruckus.
The father's hand in the third stanza is described as "battered," having been hit again something. This, along with "a palm caked hard by dirt" could imply put together that the father has fallen multiple times when stumbling drunkenly around, or battered his hand punching things in fury towards the child. He holds the child close enough so the his ear is scraping against his belt buckle, which could either be so that he doesn't get away or just holding him close as they play. The last stanza could imply he either gives the child one more beating before sending him off to bed, or pats him roughly on the head in saying that it is time to head to bed.
I enjoyed the ambiguity of the poem in being able to read it two different ways. In either context, the last two lines of the poem which read, "Then waltzed me off to bed/Still clinging to your shirt" shows the child's love and compassion for his father. If the father has indeed beaten him, he still wants to hold on to his father, a sign of unconditional love.