Kagome would probably be shocked at first. Then she would start yelling at Inuyasha, demanding to know why he's doing this. She's not the type to just sit there and take it.
Inuyasha would probably be very angry at first. He has always had a possessive streak when it comes to Kagome. He might see Koga as a rival and try to fight him. But as time goes on, he could start to realize that Kagome is happy with Koga and, though it would be difficult for him, he might eventually back off and respect her choice.
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 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.
In fanfiction, their relationship develops gradually. They start with a bit of mistrust, especially Inuyasha who is guarded. But as they go on adventures together, they begin to rely on each other more. Kagome's healing powers and her ability to see the good in Inuyasha are key factors.