Ostensibly, upon an initial reading, the tone of the poem seems to be rather whimsical and affectionate. The speaker describes a dance between himself and a figure whom we might assume to be his father. The father seems to be a clumsy but affectionate dance partner, missing steps but "waltz[ing]"...
the son "off to bed." The speaker also describes himself "clinging" to his father's shirt, suggesting that the son feels affection for his father.
However, upon a second, closer reading, it seems like the dance might be a metaphor for a different kind of relationship altogether. The dance might be a metaphor for an abusive relationship. The father is drunk, so much so that "The whiskey on [his] breath / Could make a small boy dizzy," and there are suggestions throughout the poem that the father is physically abusive towards the son. The father holds the son by the wrist, rather than by the hand, and the father's hands are "battered on one knuckle." The father also "beat[s] time" on the son's head, the word "beat" implying violence and force. In the light of this interpretation, we might infer that the speaker is confronting his father about the abuse he has suffered at his hands, and the tone of the poem thus becomes angry, accusatory, and confrontational.
The poet has used a dance metaphor to initially suggest an affectionate tone, perhaps to reflect the fact that child abuse is often hidden and unseen. Thus, what might at first seem like an affectionate dance (and relationship) between the son and his father is revealed upon a second reading as a tussle or a fight, fraught with physical abuse.