They would become more united as they are co - parenting. They would have to communicate more often about the child's upbringing, training, and future. Their relationship would likely become deeper and more complex as they share the joys and challenges of raising a child.
I've read one where the OC, reborn as Kakashi's child, had some sort of special chakra ability that was a result of their rebirth. It was really interesting to see how the author incorporated that into the Naruto universe. The story also delved into the relationship between Kakashi and his child. Kakashi was shown as a very protective but also a strict father, trying to train his child to be a great ninja. Another aspect that was well - written was the OC's interactions with Naruto and Sasuke. They became friends and had adventures together, which was really engaging.
One common theme is self - discovery. The OC, being in a new world and having a new identity as Kakashi's child, often has to figure out who they are in this new context. Another theme is family. It explores the relationship between the OC and Kakashi, how they interact, and how Kakashi influences the OC's growth. There's also the theme of adapting to a new culture. The Naruto world has its own set of rules, values, and ways of life, and the OC has to adapt to that.
Well, perhaps the child in the 'kakashi and sakura child fanfiction' gets involved in a mysterious mission that only they can solve because of their special heritage. The child could be the key to uniting two feuding ninja clans, using the influence of Kakashi and Sakura in the ninja world. Also, the story could focus on the child's relationship with their peers, who may be in awe or jealous of their powerful parents.
It could be that in the fanfic world, Sakura received some advanced training or magical knowledge that enabled her to perform such a feat at a young age. Maybe there was a unique circumstance that triggered her healing powers specifically for Kakashi.
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
In such fanfiction, the Kakashi OC often has unique physical features. For example, they might have distinct hair color or eye shape that sets them apart.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
Often, Naruto is paired with Kakashi in such fanfictions. Their bond from the original series can be explored in new ways in the context of Kakashi's reincarnation. For example, Naruto might be the one to discover Kakashi's reincarnated form and help him adjust.
Kakashi could use his Sharingan to analyze Obito's moves and find a weakness in his defenses. Since he has the Sharingan, he might be able to predict Obito's attacks and counter them effectively, eventually finding an opportunity to break free.