It could be that Inuyasha kidnaps Kagome as part of a deal. He made a deal with another powerful being to save someone else he cares about. He doesn't want to do it but feels he has no choice. Kagome, being the strong - willed person she is, then tries to find a way to get out of this situation while also helping Inuyasha out of his moral dilemma.
Well, perhaps Inuyasha is under some sort of dark spell. He might be influenced by an evil force that makes him see Kagome as a threat to his freedom or something he needs to control. So, he kidnaps her and takes her to a remote place. Kagome, being the strong - willed character she is, tries to reason with him and break the spell's hold on him.
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.
At first, their relationship would be severely strained. Kagome would be angry and scared, feeling betrayed by Inuyasha. She might not trust him at all anymore.
Inuyasha would also be worried about Kagome's safety. He knows how devious Naraku can be. He might call out to Kagome as he gets closer to Naraku's lair, hoping to hear her voice and know that she's still alive. His reaction would be a mix of anger, worry, and determination to rescue the woman he loves.
One possible plot could be that Sesshomaru kidnaps Kagome because he believes she has some power or knowledge that could be useful to him. Maybe he thinks she can help him find a powerful weapon or a way to gain more territory. He might keep her in his lair and at first be very cold towards her, but as time passes, he starts to see her in a different light.
Perhaps in the fanfiction, Koga kidnaps Kagome believing she has some special power that can help his wolf demon tribe. He might think that she can heal the sick among them or bring good fortune to their land. However, Kagome doesn't actually have this power, and she has to convince Koga to let her go while also trying not to anger him too much. As she's held captive, she might learn more about the wolf demons and their way of life, which could be an interesting aspect of the story.
One possible plot twist could be that Whitebeard actually kidnaps Luffy to protect him from a greater danger that Luffy is unaware of. Maybe there's a powerful enemy lurking in the shadows that Whitebeard knows will target Luffy soon, so he takes this extreme measure to keep him safe in his own territory.
Some great Inuyasha and Kagome fanfictions include those that focus on their adventures after the end of the series. For example, 'A New Beginning' which shows them building their life together in the feudal era. It has really good character development and stays true to their personalities.
One plot idea could be that Inuyasha and Kagome are paired up for a college project. They start off bickering like in the original series but gradually grow closer as they work together. They could discover a hidden mystery on campus that relates to their past lives.
Kagome would most likely be very angry at first. She's used to being in control of her own life and suddenly being kidnapped by Sesshomaru would be a huge violation. She might try to use her spiritual powers to fight back or at least escape.