Well, it could be that Hinata says something really cruel to Naruto by mistake. For example, she might tell him that she was only being nice to him all along because she pitied him. Naruto, who has always valued her kindness and what he thought was her love, would be devastated. His whole world view of their relationship would shatter, and his heart would break into pieces.
Naruto might become more withdrawn. He's used to being this energetic and positive person, but after having his heart broken by Hinata, he could lose that spark. He might stop going out as much, avoid his friends, and just keep to himself.
Another possibility is a complete character distortion in the fanfiction. The writer might decide to create a 'bad Naruto' version where he has lost all his positive traits. However, this is quite far - fetched considering the strong foundation of Naruto's character in the original series. It would be a very different and probably controversial take on the Naruto - Hinata relationship.
In the fanfiction, since Naruto has Kurama, he has a great source of chakra. Hinata with Nibi might also have enhanced abilities. They could team up against common enemies. Naruto's brash and bold nature combined with Hinata's calm and gentle demeanor, along with their newfound powers from Kurama and Nibi respectively, would make for an interesting dynamic. Maybe they would develop new jutsus together that utilize both Kurama and Nibi's powers.
One way could be through their leadership. Naruto, with his experience and strength, and Hinata, with her kind heart and support. They could start by gathering the remaining Uzumaki clansmen. Then, they might use Naruto's influence to get resources from the other villages. Hinata could help in planning the layout of the rebuilt village, making it a place full of love and harmony, just like her own family environment.
In some fanfiction, this could happen due to a misunderstanding. Maybe Hinata is forced into a situation where she has to seem like she's betraying Naruto. For example, she could be blackmailed by an enemy who threatens the safety of the village or her family. Another possibility is that there is some sort of mind - control involved that makes her act against Naruto.
In this fanfiction, Naruto might gain new and unexpected powers. Since the seal is broken, the Nine - Tails' chakra could be unleashed in a more uncontrolled way, leading to both challenges and opportunities for Naruto. He may have to quickly learn to master this new - found power or face being consumed by it.
In the fanfiction, it could be that Hinata is already proficient in kenjutsu. She then teaches Naruto some of the basics. As Naruto learns, they start to have a better understanding of each other's fighting styles. This could lead to them working together more effectively in future battles and also in their relationship development.
In a fanfiction, they could be involved in a race. Naruto's speed, Sasuke's sharingan - enhanced perception, and Hinata's byakugan - aided navigation could all play a part. Maybe they start off competing against each other but then realize that there's an outside threat during the race. So they put aside their differences and work together to overcome the threat, forging a stronger bond in the process.
The fanfiction could show how their relationship deepens during the pregnancy. They could have more quiet, intimate moments together, like sitting on the porch at sunset and talking about their hopes for their child. Hinata could share her dreams of their child growing up strong and kind, like Naruto.
Well, it could be that they have a sleepover at Hinata's place. They might cook a simple meal together like ramen. And then, while sitting around, Naruto could accidentally fall asleep first. Hinata might then take a moment to watch him sleep peacefully, blushing a bit as she realizes how much she cares for him. Later, she might cover him with a blanket and quietly go to sleep herself.