They could face challenges from the ninja world's authorities who might see them as deserters. Other villages might try to capture them to gain an advantage over Konoha.
Sasuke might face the challenge of understanding baby Naruto's needs. Since he's not used to dealing with infants, things like feeding, changing diapers could be really difficult for him.
He might face new and powerful enemies. In fanfiction, there could be hidden threats in the outside world that are different from those in the village. These enemies could have unique abilities that Naruto has never encountered before, testing his combat skills and strategic thinking.
He could feel a sense of guilt. Sasuke might think that his actions or their relationship issues pushed Naruto to leave. He may then set out to find Naruto, not only to bring him back but also to resolve their long - standing issues. For example, if there were unspoken words or unresolved fights between them, Sasuke would see this as an opportunity to set things right.
One big challenge would be public relations. Sasuke has a dark past, and some villagers might not trust him completely. Also, he's not as naturally warm and approachable as Naruto. He'd have to work on that. Another challenge could be dealing with the paperwork. Sasuke is used to being out in the field, not sitting behind a desk. And he might face opposition from some of the more traditional ninja clans who don't like his new ideas for the village.
One challenge Naruto might face is Sasuke's own will. Sasuke may be so consumed by his thirst for revenge or his dark path that he doesn't want to be brought back. Naruto has to break through that mental barrier. Another challenge could be the external forces that are influencing Sasuke, like the people or organizations that have turned him to the dark side. Naruto has to deal with them as well.
In a fanfiction, after their wedding, Sasuke and Female Naruto might face the challenge of balancing their duties. Naruto might want to focus on village improvements while Sasuke may be more interested in security matters. This difference in priorities could lead to arguments. Also, Sasuke has a dark past that still haunts him at times. His nightmares could potentially affect their relationship. Moreover, they will have to deal with the expectations of the village. People will look up to them as a couple, and any mistake they make could be highly scrutinized, adding stress to their married life.
One challenge could be Sasuke's resistance. Sasuke might be so set in his own ways that he doesn't want to be 'taken in' by Naruto. He may see Naruto's attempt as an intrusion on his freedom.
One possible theme could be revenge. If the writer is bashing Sasuke, they might have Naruto seek revenge on Sasuke for his actions in the original story, like when Sasuke left the village. Another theme could be power display, showing Naruto's overwhelming power as he destroys Sasuke.
In such a fanfic, Naruto might first feel extreme betrayal. He has always considered Sasuke a close friend or more. If Sasuke cheats on him, he could feel that his world has crumbled. He might initially go into a state of shock, unable to believe what has happened. Then, the thought of suicide could creep in as he might feel that there is no one left to trust or that his life has lost its meaning without Sasuke's loyalty. However, Naruto is also a strong - willed character, so he could also choose to rise above it and prove to Sasuke and himself that he doesn't need such a person in his life.
Maybe in the fanfic, Naruto could be influenced by some false information. He might believe that Sasuke has become too far gone and that there's no hope of saving him, so he abandons him.