This is one of my favorite poems because it leaves room for two very different interpretations, and I think it would be interesting to choose one of those interpretations and then base your thesis statement off that. Let's consider the evidence first.
On one hand, there is evidence that the narrator is reflecting back on an abusive childhood at the hands of an alcoholic father. Those who choose this interpretation will point to the mother's displeasure with the rowdy scene, the smell of whisky that is strong enough to make the narrator "dizzy," and the battered knuckle, indicating that the father has come home from a fight. The tone is thus dark, furthered by word choice such as this:
You beat time on my head
He didn't tap out the rhythm of the music—he beat it. That's a pretty strong and violent sounding word choice.
But not everyone reads the poem this way, and some believe that this is a loving scene of a father and son at the end of a long work day. This poem was written in the late 1940s, and a father returning home from work with whiskey on his breath would not have necessarily been cause for alarm. Fathers during this time period often worked jobs requiring manual labor, so a battered knuckle and dirt-covered palms supports that historical context. This interpretation also points to the familiar and loving use of "papa" to reference his father and to the fact that after this boisterous scene is finished, the son clings to his father's shirt as he is taken to bed, another loving gesture in itself.
Therefore, your thesis could be structured like this:
Although some believe this is a poem with evidence of an abusive childhood, the historical context and characterization in the poem indicate a loving father-son relationship.
(You could also flip this if you agree that this is a poem recalling the abuses of childhood.)
Your body paragraphs could then follow that thesis: one paragraph about the invalid (in this thesis) evidence of abuse, one examining the poem from its historical context, and a third examining the characterization of the father.
I hope this helps organize your thoughts. Good luck!