The comic shows that Zuko's mother was forced to go into hiding to protect herself and others from certain powerful forces. It's a pretty intense storyline.
Obviously, Goku is the most important character. Then his parents, Bardock and Gine. Bardock was a powerful Saiyan warrior, and Gine was a kind - hearted Saiyan. There might also be other characters like Goku's friends on Earth who could be involved in the story in some way, for example, they could be witnesses to the reunion or help Goku's parents adjust to life on Earth.
Well, in the 'Goku reunites with his parents fanfiction', it could start with a sudden appearance of his parents. They might come back through some kind of time - space rift or a special wish on the Dragon Balls. Once reunited, Goku's parents would surely be proud of him. They might help him face a new and powerful enemy that Goku alone couldn't defeat. And there would be a great family dynamic, with hugs and tears all around.
Well, first of all, Naruto would be in shock. But then he would feel an indescribable joy. His father, Minato, could teach him some new and powerful jutsu that only the Fourth Hokage knew. And his mother, Kushina, would probably smother him with hugs and tell him how proud she is of him. They could also help Naruto understand his Uzumaki heritage better.
He could also be hiding his injury to avoid being a burden. In the world of the fanfiction, his comrades might already have a lot on their plate, and he doesn't want to slow them down or cause them extra worry with his injury.
In a fanfiction, when Percy reunites with his mom, it could be a very emotional moment. Maybe Percy has just come back from a dangerous quest. His mom would probably hug him tightly, tears in her eyes. She might cook his favorite meal right away, and they would sit down and Percy would start telling her all about his adventures.
In this kind of fanfiction, Naruto might first be in shock. He has grown up without his family for so long. He could break down in tears of joy when he sees his father and mother. They would probably embrace tightly. His father might share some of the family's secrets or jutsu with him that were passed down. And Naruto would finally feel complete, having the family love he always longed for.
It might develop by Naruto exploring his family's past through his parents' memories. They could show him places important to the Uzumaki clan that he never knew about. Also, Naruto could introduce his parents to his friends, like Sasuke and Sakura, and there would be some really heart - warming interactions.