Perhaps an old enemy of Naruto's who resurfaces and decides to target his family. This could be someone who was defeated by Naruto long ago but has now grown stronger and wants to cause harm to his loved ones. They might also see Kakashi as a threat in protecting the family.
There could be a new, mysterious organization that views Naruto's family as a threat to their plans for the ninja world. Since Kakashi is always around Naruto's family, they see him as an obstacle as well. This organization could have some unique powers or motives that drive the conflict in the fanfiction.
Perhaps a powerful shinobi from another village who has a special grudge against the Leaf's ANBU. He targets Kakashi and Naruto specifically because of their reputation within the ANBU. He has unique abilities that pose a great challenge to them, like the ability to nullify ninjutsu for short periods.
Danzo could be a great antagonist. If Kakashi travels back in time, Danzo's underhanded plans, like his control over Root and his desire for power, would still be in motion. He'd likely oppose Kakashi's attempts to change things for the better, especially if it threatened his own influence.
Danzo could also be a possible antagonist. He might have his own plans for the Chunin Exam, perhaps trying to manipulate the results to get certain genin under his control. His shadowy and self - serving nature would create a lot of conflict, especially when Kakashi and Naruto start to suspect his motives.
It could be a rogue ninja who has a vendetta against Shizune's family. This ninja might see Naruto as an obstacle in his path to revenge. He could target Naruto to get to Shizune and try to break their family - like bond.
Maybe an organization that wants to use her unique abilities. If she has inherited some special power from Kakashi or has her own distinct skills, an evil organization could try to capture her and force her to work for them. They would be the main obstacle she has to face in the story.
It could be Orochimaru. He might be interested in the unborn child for some dark experiment, thinking that the child of Kakashi and Rin could possess some unique abilities. He could send his minions to spy on them or even try to kidnap Rin.
It could be Orochimaru. He might see the baby versions of Team 7 as perfect subjects for his experiments. He could try to kidnap them to use their unique chakra or potential for his own dark purposes.
It could be a relative from his family who was behind the abandonment. Maybe they want to keep Naruto away from some family secret or power, and they will do anything to stop him from finding out the truth.
Maybe it's an evil organization that wants to isolate Naruto. By making his family forget him, they hope to break Naruto's spirit and prevent him from becoming a powerful force in the ninja world. So they target his family's memories as a way to get to him.
It could be a powerful rogue ninja who has a vendetta against Kakashi and sees his daughter as a way to get revenge. This antagonist might try to use her as a bait to lure Kakashi or Naruto into a trap.