Situational irony, of course, is the difference between what we, as readers, expect to happen vs. what actually happens. We can find situational irony in "The Peaches" in the hypocrisy of the characters.
First let's look at the hypocrisy in Dylan's cousin, Gwilym. Gwilym is always seeking to be like the adults (who are also always hypocritical). This suits Gwilym well. He wants to be a preacher (and is always creating sermons and forcing people to confess sins) yet participates in questionable sexual behavior in the bathroom.
Then we have the hypocrisy of the adults, especially Aunt Annie and Uncle Jim. Aunt Annie is always obsequious. Acting one way but feeling another, she takes out her coveted canned peaches that she has been saving for a year to serve to guests. Uncle Jim picks Dylan up for his visit, but leaves him for HOURS in an unsafe alley in order to drink at a bar! Later, Dylan and Jack discover that Uncle Jim has sold one of his own pigs to use the money for his liquor addiction. Uncle Jim also overreacts to his guests' treatment of the peaches:
Who does she think she is? Aren’t peaches good enough for her? To hell with her bloody motor car and her bloody son! Making us small.
Finally, we have the hypocrisy of Mrs. Williams herself as she comes to pick up Dylan to take him back to Swansea. Jack grabs Mrs. Williams and explains all of the horrible truths: Uncle Jim's threats of abuse, Gwilym's tortures, Dylan's attempts at thievery, and Aunt Annie's mistreatment of Jack's jacket. Another irony here is not all of this is truth. The second irony is that, of course, as a hypocritical adult, Mrs. Williams does absolutely nothing. Therefore, the story certainly ends on a note of disillusionment due to its ever-present irony.