Our speaker is the "small boy" in the second line. He's probably up late, complaining about having to go to bed when his parents are still up. Maybe he's even been forced into cozy pajamas, ready to hop into bed. But right before he does, he gets to dance with his dad.
We're not sure, though, whose idea this dance was – the kid's, or his drunken father's. The boy is being made dizzy by the alcohol on his dad's breath, and the speed of this waltz, which is more like a romp than a serious ballroom dance. His ear keeps getting scraped, and his dad keeps the beat on the boy's head, with rough hands.
The whole time, the boy is a little nervous about annoying his mother, and is getting a little roughed up by his dad, but he hangs on to his father anyways. Even when his dad dances him all the way to bed, he still wants to cling on to this whirling, waltzing man that he loves, no matter how much his breath smells like whiskey, or how battered his knuckles may be.