Some fanfics might explore their relationship by giving them a shared mission. They have to work together to save the village or something similar. During this mission, they get to know each other better, not just as mother - son but as comrades. They learn about each other's strengths and weaknesses, which deepens their bond in a very unique way.
It shows a contrast to the normal mother - son relationship. Instead of the loving and protective Kushina, here she is evil, which makes Naruto question his own identity and family bonds.
It could show Minato experiencing Naruto's loneliness as a child first - hand when in Naruto's body. This would make Minato understand Naruto's pain on a deeper level. Then, when Naruto is in Minato's body, he could see how much his father was respected and loved, which would strengthen their bond in a new way.
Fanfiction can explore their relationship by delving into their unfulfilled time together. For example, showing how Minato and Kushina would have raised Naruto. It could also explore their shared experiences, like how they all have a connection to the Nine - Tails. Maybe in fanfiction, they have family adventures where Naruto learns from his parents' skills and wisdom.
A unique way to develop their relationship could be through a series of challenges. For example, they are trapped in a mysterious dimension together and have to rely on each other to escape. In the process, they discover each other's strengths and weaknesses, and Kurama realizes that Kushina is not just Naruto's mother but a powerful ninja in her own right. This mutual respect and reliance would strengthen their relationship.
One way is by exploring their cultural differences. Vegeta is from an alien race with its own values and traditions, while Bulma is an Earthling. The fanfiction could show how they introduce parts of their respective cultures to each other and how that enriches their relationship.
Another unique exploration could be through a shared goal that is not related to the main Naruto plot. For example, they both want to protect a special place in the spirit world that has significance for the Nine - Tails. To do this, they have to work together in a way that they haven't before. Naruto has to use his human skills and the Nine - Tails has to use its tailed - beast powers in harmony. This would show a different side of their relationship, one based on mutual respect for each other's abilities.
They could be involved in a cross - dimensional adventure. Maybe Naruto accidentally opens a portal to a dimension where Kushina is still alive but in a different situation. They then have to adapt to this new world together and in the process, their relationship evolves. It could involve learning new skills from each other and facing strange creatures. Also, their communication could be a key factor. If Naruto starts to communicate with Kushina in a different way, like through a special Uzumaki - only form of telepathy, it would be a unique aspect of their relationship development.
Some fanfictions might explore their relationship through time - travel. For example, if Cedric could go back in time and help Harry in his earlier years at Hogwarts. This would not only change the course of some events but also show a different side of their friendship, as Cedric would be the more experienced one guiding Harry.
One unique way to develop their relationship is to have them go on a journey through different time periods in the magical world. As they experience different eras together, they see how their relationship might have been in different circumstances and this deepens their connection in the present.
One way to develop Naruto's character uniquely is to put him in a situation where he has to protect both Mikoto and Kushina at the same time. This would force him to use his skills in new and creative ways. He might also have to make difficult decisions between protecting them and fulfilling his duties as a ninja. For Kushina, her character could be developed by showing her interacting with the other villagers after being resurrected. She was a strong - willed woman, and seeing how she copes with the changes in the village could be interesting. Mikoto could be developed by having her mentor Naruto in some Uchiha - specific skills, which in turn helps Naruto understand the Uchiha better and also strengthens their bond.