This is pretty much as it happened, with a bit of editing, of course. What you don’t see the boy trying to turn over mid-change and putting his hands in the “danger zone” and his father’s frustration. Diaper changing used to be rather pleasant – singing, laughing – until he started moving. Now it’s toxic waste alligator wrestling.
(The whole “Charles Dickens” thing reminds me of Monty Python’s “Bookshop Sketch” from their Contractual Obligation Album, which is very similar in form to their famous “Cheese Shop Sketch.” If you’re this flavor of nerd, you need no further information. If you’re not, any explanation would seem like a colossal waste of your time.)