It could be Orochimaru. He might have manipulated Kushina into kidnapping Naruto. Orochimaru has always been interested in the power of the Uzumaki clan and Naruto's nine - tailed fox power. He could be using Kushina as a tool to get to Naruto.
Another possibility is that there is no real antagonist in the traditional sense. Kushina herself could be seen as the source of conflict as she kidnaps Naruto out of her own misguided beliefs. However, if we consider external factors, it could be a group within the Hidden Leaf Village who oppose Naruto's growth and have used Kushina's love for him to make her take this drastic step.
Perhaps the antagonist is a new, unknown enemy who has a vendetta against the Uzumaki family. This enemy has somehow influenced Kushina and made her kidnap Naruto. The enemy could be after Naruto's power to use it for some evil plan, like destroying the Hidden Leaf Village.
Maybe in the fanfiction, Kushina kidnaps Naruto because she believes she can protect him better away from the Hidden Leaf Village. She thinks the village has become too dangerous for him. However, Naruto doesn't understand her intentions at first and struggles against her. As the story progresses, he realizes her love and the real reason behind her actions.
It could be Orochimaru. He's always been interested in powerful ninja and their abilities. Since Kushina has strong chakra and a connection to Naruto, Orochimaru might see her as a valuable asset to either experiment on or use as bait for Naruto. He's devious enough to come up with a complex plan to capture her.
It could be that there is no traditional antagonist. The conflict might be internal, with Naruto's own emotions towards Kushina being the main source of drama.
It could be someone who took advantage of Kushina's leaving. Maybe a rogue ninja who wants to use Naruto's vulnerability to their advantage. They could try to turn Naruto against the village by making him believe that the village drove Kushina away.
Another possibility is that an old enemy of the Uzumaki clan resurfaces. They use Itachi's complex relationship with the village and his own motives to manipulate him into kidnapping fem Naruto. So, this old enemy would be the main antagonist as they are the ones driving the overall conflict.
It could be an old enemy of Kushina's who was thought to be dead but has now returned. Maybe someone from her days in the Uzumaki clan who has a vendetta against her and now sees Naruto as an obstacle too.
Maybe an evil organization that wants to use Naruto's power and the connection he has with Kushina for their own dark purposes. They see Natsumi as an obstacle in their plan because she is always by Naruto's side. This organization could be experimenting with dark jutsu and need Naruto's chakra and Kushina's latent abilities (passed on to Naruto) to complete their evil experiments.
Another aspect could be that the fanfiction delves into how Kushina's presence affects Naruto's relationships with others. For instance, his relationship with Sasuke could be different. With a strong maternal figure in his life, Naruto might be more stable emotionally and be able to approach Sasuke in a more understanding way, which could potentially change the whole dynamic of their rivalry and friendship.
It could be a new, powerful dark wizard who has a grudge against Fairy Tail. This wizard might manipulate Natsu into kidnapping Lucy to create chaos within the guild. The dark wizard could be after some powerful magic that only Lucy can access, and by kidnapping her, they hope to force her to give it up.
Well, Vegeta himself could be seen as the antagonist in the beginning. Since he is the one doing the kidnapping, he's causing distress to Bulma. However, as the story progresses, the real antagonist could turn out to be someone else. For example, another alien race that is after Vegeta and uses Bulma as bait to lure him into a trap. So, it's not so straightforward in a fanfiction.