The whiskey on your breath Could make a small boy dizzy; (lines 1-2)
Whiskey is traditionally considered a manly drink. So that the father drinks whiskey hints that he's macho. However, this man's son, even though a male, is made dizzy by the whiskey – and perhaps the masculinity – of his own father. This is an effective way to establish the ages of these males – one is a man, and one is just a boy.
We romped until the pans Slid from the kitchen shelf; (lines 5-6)
This is not a beautiful dance, but is one chock full of horseplay and romping. This dance is masculine and rough. Don't forget that in a normal waltz, there is a male and female partner. There's no female here. Instead, a little boy is being spun around in the female role.
My mother's countenance Could not unfrown itself. (lines 7-8)
The mother's feminine disapproval provides a contrast to the masculinity of her husband and her son, who are making a big ruckus. Either she's enjoying watching them, or wants to protest but is following traditional gender roles by remaining subservient to her husband.