Symbolism, Imagery, Allegory
Peter's not jumping up and down at the chance to go shoe shopping—especially not if it's with his mom and his annoying little brother. But he doesn't have a choice in the matter, and so off they go. Peter initially picks out the shoes he always gets, but Fudge throws a tantrum when he's asked to try on saddle shoes. He wants to be just like his big brother:
Fudge sat up. "Like Pee-tah's." he said.
I smiled. I guess the kid really looks up to me. He even wants to wear the same kind of shoes. (6.93-94)
In this moment, it's clear that even though Fudge is annoying as can be, he often just wants to get Peter's attention and approval. And even though Peter always gripes about Fudge and how he doesn't want to hang out with him, he still does the good big brother thing and tries on the saddle shoes so that Fudge can see him wearing them:
Mr. Berman came back with a pair of brown-and-white saddle shoes in my size. I tried them on. Did they look ugly.
"See Peter's nice saddle shoes," my mother said. "Now Fudgie tries on his nice saddle shoes.
Fudge let Mr. Berman get him into his new pair of shoes. (6.114-116)
Of course, Peter doesn't actually end up buying the shoes, but he does humor Fudge. He knows in his heart of hearts that Fudge isn't actively trying to make Peter's life miserable; he just doesn't know any better. He worships his big brother and wants to be like him. Peter's more grownup shoes are another symbol of his maturity, like the lock on his bedroom door.