At first, Kagome is likely to be angry. She's a strong - willed character, so being kidnapped goes against her nature. She would probably struggle and try to escape immediately, yelling at Koga about how wrong his actions are.
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 can be really interesting in this context. His reaction to Kagome's transformation into a Dark Miko would be complex. He's used to the normal Kagome, so seeing her change might make him both worried and a bit on edge. He could try to bring her back to her old self while also being in awe of her new power.
Well, often there is a theme of family acceptance. Since this is a non - traditional family situation, the fanfics may explore how Sesshomaru's family or Kagome's family back in her own time deal with the news. There could also be a theme of protecting the unborn child. Given the dangerous world they live in, with demons and all, both Kagome and Sesshomaru would need to ensure the safety of their baby. Additionally, the theme of changing relationships is common. Their relationship might start as an unexpected or even hostile one and then transform into a more loving and protective one because of the pregnancy.