Dudley called Harry up out of the blue in a panic when his two year old starts showing signs of magic. Like how does he stop her from sneezing and setting the curtains on fire?
Dudley and his family visit the Potters at Christmas and Dudley finally agrees to let his kids try out James' new toy broomstick and they end up crashing into him (Dudley) and knocking him over.
Dudley explains to his parents that he is sending their granddaughter to Hogwarts with Harry's son Albus and if they ever call her or Harry's family freaks, he will never speak to them again.
Harry explains how wizarding currency works to Dudley when he tries to buy his daughter, Petunia Jr.'s, wand with a Debit card.
Harry then shows Dudley and his wife around Diagon Alley, keeping them far away from Weasley's Wizard Wheezes.
Dudley congratulates his daughter on making it into Hufflepuff, whatever the hell that meant.
Dudley didn't quite understand what it meant to be a Prefect, but he was proud anyways.
Dudley eventually learned to accept what he doesn't understand and to not be afraid of what others can do just because he can't.