It says in Goblet of Fire that Dudley bullied students at Smeltings. I am sure that Dudley also engaged in bullying in elementary school, and I believe Dudley's elementary school should have contacted his parents as happens in this chapter. This would never have happened in canon because Petunia would never have been like this and was in denial about Dudley's behavior, but this is what should have happened.

Petunia Dursley was quietly sitting on her Lazy Boy recliner doing crossword puzzles when her telephone rang.

Petunia calmly got up and answered the telephone, hoping that her bestie Yvonne would be on the other end.

"Petunia Dursley speaking," said Petunia clearly.

"Hello, Mrs. Dursley," replied a male voice, "My name is Ethan Educate and I am Dudley's kindergarten teacher. There have been issues with Dudley at school today."

"Did my Dudders get hurt or sick?" asked a suddenly worried sounding Petunia.

"Nothing like that," said Professor Educate reassuringly, "However, we have some concerns about Dudley's behavior."

"Dudders is a boisterous little boy, but he wouldn't hurt a fly," replied Petunia defiantly.

"That's not what his behavior today has led us to believe," said Professor Educate in a very serious voice.

"What about Dudley's behavior is causing such serious concerns?" asked Petunia urgently.

"Before class," explained Professor Educate, " Dudley demanded that a girl give him all of her lunch money and threatened to make her see stars if she didn't do so. When the girl refused, Dudley punched her in the face as hard as he could, leaving her with a broken nose and a bloody face."

"Oh, my!" gasped Petunia.

"Then," continued Professor Educate, "During student introductions at the start of class, Dudley insulted several of his classmates with demeaning names. He called one boy fat, another girl stupid, and another boy the U word."

"Is that it?" inquired Petunia hopefully.

"No," answered Professor Educate, "At recess, Dudley intentionally shoved his own cousin Harry Potter down from behind as hard as he could, resulting in Harry falling hard on the sidewalk and breaking his glasses. Dudley has been isolated for the day. I should warn you that if this pattern of behavior continues, Dudley will face suspension from this school. I urge you to have a very serious conversation with Dudley tonight about his behavior."

"I will," promised Petunia.

"Good," said Professor Educate, " I have to go now. Have a nice afternoon."

Professor Educate hung up.

...

It was dinnertime and Vernon, Petunia, Dudley, and Harry were just sitting down to a delicious dinner of spaghetti with meat sauce mixed in, breadsticks, and Coca Cola Classic to wash it down with when Petunia asked Dudley, "How was school today?"

"Fine," said Dudley in an innocent sounding voice.

Turning to Harry, Petunia asked, "Harry, did Dudley bully other children at school today?"

"Yes," confirmed Harry, "At the start of the day, Dudley ordered a girl to give him her lunch money and threatened to make her see stars if she didn't do so. When she refused to do so, Dudley punched her in the face as hard as he could resulting in the girl ending up with a bloody face and a broken nose. During student introductions, Dudley insulted the other kids by calling them names such as fat, stupid, and the u word. And at recess, he shoved me as hard as he could from behind causing me to fall on the sidewalk and break my glasses."

"This is consistent with what Professor Educate told me on the telephone," said Petunia in a businesslike voice, "Dudley, do you deny bullying your classmates?"

"No," smirked Dudley, "I'm going to bully those assholes and bitches and assert my status!"

"No, you are not," countered Petunia.

"It's not a good reflection on our family to have a bully in the family," piped up Vernon.

"That's not the point," replied Petunia calmly, "It's about Dudley's character and the kind of person he is going to be. I should warn you, Dudley, that Professor Educate told me that further bullying behavior on your part could result in your suspension from school. Furthermore, I should inform you this nanosecond that if I receive another call from Professor Educate that you have been bullying your classmates, I will punish you at home by banning you from watching TV or playing computer or video games for a month and your allowance will be suspended to pay for any damages you do to your victims property, be it their glasses or whatever, until such time as the replacement cost is paid off."

"I'll just have to not get caught then," said Dudley smugly.

"It's inevitable that you will," said Harry warningly.

"Harry's right," said Petunia clearly, "Especially since after today the adults at school will be keeping a closer eye on you."

Dudley sighed in defeat.

"Instead of acting defeated," said Petunia briskly, "Try putting yourself in your victims' position. Think about how you would feel if someone threatened you, punched you, called you insulting names, or shoved you to the ground."

Dudley fell silent and had a thoughtful look on his face for five minutes and five nanoseconds.

"Mom, you're right," said Dudley quietly.

"Dudley, I'm going to give you some advice," said Petunia clearly, "Instead of bullying and asserting your status, how about being nice to your classmates and trying to make friends."

"It's not too late," added Harry encouragingly, "Apologize to your classmates tomorrow and I suspect most of them will forgive you. Here's the thing though. Most people follow the rule of reciprocity. That means most people treat other people how the other people treat them whether that is nice, mean, or somewhere in between."

"An excellent point, Harry," said Petunia approvingly, "If you are a kind person, it will come back to you. If you are a jersey, it will come back to you. Start being nice to your classmates tomorrow and you'll make some great friends. That's a lot more satisfying than dominating people by being a bully. Maybe once you've made friends, you can invite over to the house to play with you and maybe they'll invite you to their houses too."

Dudley smiled at that.

"I look forward to making friends," said Dudley finally.

Petunia's intervention had been successful.