How does P. G. Wodehouse mock the system of social class of Britain in his short story, "The Custody of the Pumpkin"?
This is an awkward question to answer because there are a couple of errors in the question itself. The first is that this is not a short story, though seemingly well anthologized, but a chapter from Wodehouse's novel, Blandings Castle. The anthologized portion is actually "Chapter 1: The Custody of the Pumpkin" of Blandings Castle (1935). Though anthologized, its origins and context need to be understood and recognized in order to have a fair perspective on it and in order to analyze it correctly.
The second error is in the use of the word "mock." This is a strong word that is better associated with bullies or anarchists who attack and blindly criticize than with world renowned humorists who amuse while painting revealing pictures of human foibles.
to tease or laugh at in a scornful or contemptuous manner (Oxford Dictionary)
the feeling that someone or something is worthless or despicable; contemptible (Oxford Dictionary)
the feeling that a person or thing is beneath consideration, worthless, or deserving scorn (Oxford Dictionary)
These definitions indicate that there is real underlying hatred in something that mocks. As a comparison, contrast Wodehouse's chapter to Jonathan Swift's biting essay mocking Britain's policies in Ireland, "A Modest Proposal." You'll see that while the one by Swift mocks with scorn and contempt, the other by Wodehouse amusingly satirizes the foibles of the fading post-World War I British upper class by pointing out the incongruities between aristocratic country life and modern life.
Having said this, what are some details of how Wodehouse humorously satirizes the country life of the landed Lord after one world war has raged? To start with, (1) Wodehouse shows Lord Emsworth as completely dependent upon his domestic servants to get by: e.g., Beach must give him metaphorical sight by removing the cap from his telescope; McAllister, with the waggling red beard, must raise his pumpkin. Additionally, (2) Lord Emsworth has no understanding of nor control over his son, the Honorable Freddie: Freddie gets into debt and is banned from London; Freddie goes gallivanting in bright morning sunshine with a strange American girl with no aristocratic background (and marrying her); Freddie speaks in a slang that the "guv'nor" is hard pressed to make sense of:
Awfully sorry and all that, but couldn't hold out any longer. I've popped up to London in the two-seater and Aggie and I were spliced this morning. ... Aggie's guv'nor ... [is] coming to see you. He wants to have a good long talk with you about the whole binge. Lush him up hospitably and all that, would you mind, because he's a sound egg .... Your affectionate son, Freddie
Another very important way that Wodehouse humorously satirizes the landed, country aristocracy, that might be characterized as "dislocated," is by (3) satirizing their values as epitomized by Lord Emsworth's preoccupations with winning gardening prizes. His family has won prizes for tulips, for roses, for spring onions, but they have not won prizes for pumpkins and Lord Emsworth has committed himself to doing just that. His values are not remotely connected to the post-war world, which Donaldson, the American millionaire, is, in contrast, connected to:
"... conditions have changed very much in America of late. We have been through a tough time ... But things are coming back. ... I am a firm believer in President Roosevelt and the New Deal. Under the New Deal, the American dog is beginning to eat more biscuits. ... I an Donaldson's Dog-Biscuits."