It could be due to the current situation in the village. There might be threats that required Naruto to stay. Tsunade, as the Hokage, had to consider the overall safety and stability of the village. So, she denied Naruto's request for the training trip to ensure he was available in case of any emergency.
He might become more determined to prove himself to Tsunade. This could make him train even harder within the village. He could also start to question Tsunade's decisions and try to find ways to convince her that he is ready for such a training trip in the future.
In such a fanfiction, Naruto might return to the village with new and powerful jutsu. He could surprise his friends with his enhanced skills. For example, he might be able to create new types of shadow clones or have a better control over his chakra. Maybe he would also have new insights on how to deal with his enemies, like Orochimaru or the Akatsuki.
Well, in this fanfiction, there could be a mentor who is a former Akatsuki member. This person has seen the dark side of the ninja world and can teach Naruto about the true nature of power. Or perhaps a sage from a hidden mountain, who has lived for centuries and has vast knowledge of chakra manipulation and nature transformation. Also, a wandering samurai with a unique combat style could be a mentor for Naruto, teaching him discipline and different fighting strategies.
It's possible that the kid is a result of some sort of time - travel or alternate reality situation. Maybe the kid is actually Naruto from a different timeline or dimension, and Naruto has to figure out how to deal with this strange situation while on his training trip.
Well, it could be that the kid serves as a source of motivation for Naruto during his training. He would want to become even stronger to protect his child. Also, the presence of the kid could lead to some comical situations, like when the kid tries to imitate Naruto's training moves in a clumsy way.
Well, in this 'naruto longer training trip fanfiction', perhaps Naruto discovers a hidden village with a long - lost ninja art. He has to go through a series of trials to learn it. Or, he could face challenges related to his inner demons while on this extended journey. For example, dealing with his loneliness and self - doubt, which makes his character development more profound. Also, he might find a way to better control the Nine - Tails' power during this trip.
He could meet some old enemies who have changed their ways. For instance, some of Orochimaru's former minions might have decided to start anew and cross paths with Naruto. Or perhaps he meets a hermit ninja who has been living in isolation for years and imparts some valuable wisdom to him.
Their relationship develops as they train side by side. Naruto starts to notice Hinata's determination and strength, which makes him see her in a new light. Hinata, on the other hand, becomes more confident around Naruto.
During the training trip, they might face some tough opponents. This would force them to rely on each other and grow closer as a result. They could also discover new places with unique chakra sources that enhance their abilities.