Please note that, as I have never been in the child-services system, much less the English child-services system, I will probably get details of the system wrong. So don't take anything I say about orphanages or adoptions as fact.
Disclaimer: I am not, nor shall I ever be, JK Rowling. As such I own none of the characters that you recognize or the settings that you recognize.
It was mid-morning when the Grangers came into the building. The older kids were at school, but the younger kids were all playing in their room. Dudley wasn't playing with the other kids; instead he was sitting on his bed thinking about and wishing for a new family. Then four people walked in with Miss Nina: a tall, thin brown- haired man, a medium-height, brown-haired woman, a little girl with bushy brown hair and an overbite, and a little boy with silvery-blond hair and grey eyes. The two children clung to their parents' hands and the blonde boy stuck to his mum's side like he would never, ever let go. The little girl was holding her father's hand nearly as tightly as the little boy was clinging to his mum, but she was pulling him into the room and looking around with bright, intelligent eyes.
All of the faces in the room turned to look at the family, each pair of eyes shining in hope that this would be the family to take them home. Most of the kids who were old enough to walk and talk came over to the family and greeted them. Dudley stayed sitting on his bed, just watching. This – families coming in – had happened a number of times in Dudley's seven days at the orphanage, and only a few families had actually adopted someone. He knew from the first couple of times that it was best to wait until the first crowd of children had scattered before approaching the family.
He noticed that the bushy-haired girl had let go of her father's hand and was talking to some of the other kids. She had managed to pry her brother off of her mum and was now holding his hand as she dragged him around the group. She looked around suddenly, searching for the eyes she felt on her back, and made eye contact with Dudley. In an instant, she had said goodbye to the kid she was talking to before and dragged her brother over to where Dudley was sitting.
"Hi!" She said brightly, surprisingly clear for such a young girl. "My name is Hermione, and I am two. What is your name?"
Dudley blinked for a second, taken aback by her fast speech, then replied: "Dudley."
"Nice to meet you, Dudley! This is my brother Draco, he's almost one and a half. Mummy and Daddy say that we are getting a new sibling, if we meet someone, so Draco and I are meeting everybody!" She paused to take a breath, and then added "I want another brother. Do you want to be my brother?"
Dudley just stared at her, not quite understanding. Then her question clicked into place in his brain and he nodded.
"I would like that, I think." He said slowly. Hermione beamed and grabbed his hand, dragging him off his bed and toward her parents. Dudley stumbled, but managed to stay on his feet.
"Mummy! Daddy! Meet Dudley! He is –" she broke off, realizing she didn't know Dudley's age. "How old are you?" she asked him.
"Almost one and a half." He said quietly, shyer now that he was in front of adults.
"He is almost one and a half, like Draco! Can he be my new brother? He said he wants to be." Her eyes were full of excitement, and she was nearly bouncing up and down. Her father got down on his knees so that he was nearer to Dudley's height, though he was still taller.
"Hello, Dudley," He said kindly.
"Hello, Mister," Dudley answered shyly.
"My Hermione seems to have taken a liking to you, and she has very good taste. I'll let you in on a secret, though." He lowered his voice to a stage whisper. "She's quite a bossy little girl. Do you think you could handle her?"
Dudley nodded, glancing at Hermione as she let out an indignant "Hey! I am not bossy!"
Her father grinned at her before turning back to Dudley.
"So how would you like to be a part of the family, Dudley?"
"I would like that very much, sir!"
Dudley could hardly believe what was happening. His wish had come true! He was getting a new family!