The whiskey on your breath Could make a small boy dizzy; (lines 1-2)
These lines introduce the two main characters of this poem, the father and his son. The son is addressing his father, and referring to himself, the small boy, in the third person. His father, here, is demonstrating his dominating by smelling like alcohol, and, more specifically, like whiskey. The son, on the other hand, is small and dizzy compared to his father.
We romped until the pans Slid from the kitchen shelf; (lines 5-6)
These lines place the dance in the kitchen, which, for many, is the center of family life. The kitchen is where meals are made and shared, and where waltzes are danced that shake the pans off the shelf.
My mother's countenance Could not unfrown itself. (lines 7-8)
These lines introduce the mother of the family. Her "countenance," or facial expression, can't stop frowning. But maybe her expression isn't showing what she's really thinking. There are a few possibilities here. The mother might be putting on a frown for the sake of seeming as though she disapproves when she's actually amused by this dance. Alternatively, she's really upset, and too angry or too scared to say anything to stop this dance from making a mess of the kitchen.