The relationship would likely become more intense. They would have to rely on each other more, and their bond would deepen as they are about to become parents. Inuyasha would probably become more protective of Kagome.
In fanfiction, their emotional connection might grow as they share their past traumas. Inuyasha has the pain of being an outcast, and Kagome has lost her father. By opening up to each other about these deep - seated hurts, they become closer. It's like they are each other's safe haven where they can be vulnerable.
In fanfiction, their relationship might develop as they gradually understand each other's cultures. Inuyasha is from the feudal era and Kagome is from modern times. The clash and subsequent understanding of their different ways of life can add a lot of depth to their relationship. For instance, Kagome introducing Inuyasha to modern concepts like friendship equality, which in turn helps him open up more to her.
One possible fanfiction could be about Inuyasha in his full demon form and Kagome's journey to understand and reach out to him. Maybe she uses her spiritual powers to calm him down when he's on the verge of losing control. It could explore their relationship dynamic in this unique state of Inuyasha.
In many fanfics, Kagome is often portrayed as even more brave than in the original. For example, she might take on stronger demons on her own without hesitation. She is also usually depicted as having a strong sense of justice, always ready to fight for what's right.
Another interesting one is 'Inuyasha and Kagome: Domestic Bliss'. This story delves deep into the daily life of the married couple. It shows how Kagome tries to introduce some of her modern ideas into their home, like new cooking methods or ways of organizing things. Inuyasha is initially a bit resistant but then comes to appreciate these new things. It's a really cute and relatable take on their married life.
There could be a fanfic that delves into their backstories more. For instance, exploring Sango's past as a demon slayer in greater detail. How she overcame her family's tragedies and how that has shaped her. Inuyasha and Kagome could be part of this exploration, learning more about Sango and in turn, Sango learning more about their own complex pasts and how they are dealing with it.