One idea could be that Kakashi travels back to the moment right before Obito's 'death'. He uses his knowledge of future events to prevent the cave from collapsing on Obito. Then, together they are able to rescue Rin more effectively and change the whole tragic course of events.
Their relationships would become much stronger. Kakashi would no longer have to bear the guilt of Obito's 'death' and Rin's loss. Obito would be extremely grateful to Kakashi for saving his life and would likely view him as an even greater friend and ally. Rin would also be happy to have both of them by her side, and they could form a very tight - knit team.
One possible plot could be that Obito arrives just in time to save Rin from being captured by enemy ninjas. He uses his Sharingan abilities to outwit the enemies and then escapes with Rin. Maybe he has to fight through a horde of strong opponents, but his determination to save Rin gives him the strength to persevere.
One potential antagonist could be the Hidden Mist ninjas. They are known for their ruthless tactics, and they might target Rin for some strategic reason. Maybe they think she has valuable information about Konoha's defenses.
One common theme is redemption. Since they go back in time, both Obito and Kakashi often try to atone for their past mistakes. For example, Obito might try to prevent the events that led him to become evil in the first place.
There's also 'Time's Redemption'. This fanfiction has a unique take on time travel. Kakashi and Obito are sent back together. They have to work together to change the fate of the Hidden Leaf. The story delves deep into their relationship, exploring how they understand each other better through this time - traveling adventure.
One common theme is redemption. Since they both have a lot of regrets in their original timeline, time travel gives them a chance to fix things, like saving their friends or preventing the destruction of the village.
In some fanfictions, Naruto might save Obito during time travel by using his strong will and the power of friendship. Naruto could convince Obito to change his ways before he goes too far into the dark side. He might show Obito the future of the village and how his actions are causing more harm than good.
One great 'Obito and Kakashi time travel fanfiction' is 'Time's Redemption'. In this story, Obito and Kakashi are sent back in time and have to deal with the knowledge they now possess about the future. They try to prevent certain tragedies from occurring. It has some really interesting character interactions and explores their relationship in a new light.
A new character could be introduced as the antagonist. Maybe someone who has also time - traveled and has their own agenda for the past. This character could be trying to preserve the original timeline for some reason, or they could be trying to create an even worse future. They would oppose Obito and Kakashi at every turn, creating a lot of conflict and drama in the fanfiction.