This is a great question.
Two very distinct and different interpretations to this poem rise to the surface for most reading audiences. For the most part, this occurs based on our environments and positions in recent history.
This poem was written in 1948. THIS MUST BE KEPT IN MIND.
One interpretation is that this dance is a metaphor for a situation of extreme abuse. This is the often-held interpretation of a student of the late 20th century. For those born in the 80s and 90s, we see great understanding of abuse because of books like A Child Called It and the regular education of children and peers to help report signs of abuse because of its prevalence in our society. Perhaps it is more prevalent today merely because in rearing children a label has moved from spanking to abuse.
Another interpretation is one that arises from someone who is closer to the era, or from one who understands the era. That is that this is a ritual time of kinship between a father and son as part of a bedtime routine. The belief is that the poem actually uses rhythm and music terminology to assert that this was a dramatically happy event that caused mom to be jealous.
I encourage you to read the poem again looking from both of these perspectives. Words like "beat" and "romped" have various meanings for the various era. Thinking about even some of the couplets, you have innuendo that means different things in different eras. Today, we associate whiskey on the breath of a dad to mean he's totally drunk and ready to beat children. In the late 40s, a shot of whiskey was a way to relax.
This is one of my favorite poems. Roethke (the author) vividly captures the joyful bond between father and son.
The father and son in "My Papa's Waltz" have a close relationship. The father is a blue collar worker, someone who works hard with his hands; his knuckle is scraped and his hands are caked with dirt from his day's labors.
The son clearly feels his father's belt buckle scraping his ear as he "hangs on for dear life," romping (a lively word describing the playing of youngsters) in a waltz with his father—while his mother frowns at the pans rattling off the shelf. (However, we don't get the idea that she is really angry.) The boy even smells the whiskey on his dad's breath: perhaps from stopping for a drink on his way home from a long day at work.
The boy loves this time with his father: perhaps they don't have much opportunity to do this kind of thing, with dad coming home late and bedtime looming for the boy—this is what may make is so memorable for the son. And it is a memory that stays with him long after his childhood years have passed. The father beats the rhythm of the waltz on his son's head as they dance, bringing a sense of movement to the verse. The poem ends as the father waltzes his son off to bed, with the boy "...still clinging to [his] shirt."
The mood of the poem is positive and joyful, and with the imagery provided, we know the son and father enjoy each other's company greatly. The imagery and the sense of playful dancing before bed allow this sense of joy to come through to the reader, along with a sense of nostalgia from the now-grown son, who we can assume is the author of the poem.