Their relationship would be severely damaged. Harry would likely feel betrayed by Sirius. After all, Sirius is supposed to be one of his protectors. It would be a huge breach of trust. Sirius, on the other hand, would probably be filled with guilt if he realizes his mistake. He would have to work hard to regain Harry's trust, if that's even possible in the context of the fanfic.
Well, if Sirius takes Harry to Voldemort in a fanfic, it would be a huge deviation from the normal story. One possibility is that Sirius is trying to make some sort of deal with Voldemort to save others. But Voldemort is not one to be trusted. Harry, being the Boy Who Lived, is a valuable asset to Voldemort for his own dark purposes. It could lead to a tense stand - off where Harry has to use his own wits and magic, even at such a young age, to try and escape the clutches of the Dark Lord.
Well, their relationship would be in tatters. Harry would probably avoid Sirius like the plague after such an event. Sirius, on the other hand, would be at a loss for how to deal with what has happened. He might feel betrayed, even though he knows Harry was forced. This would create a huge rift between them that would take a lot of time and effort, if ever, to mend. It would also change the way they interact with other characters in the fanfiction, as their relationship was an important part of the overall story dynamic.
Sirius could use his knowledge of the wizarding world's secrets. He might know some hidden places or spells that could keep Voldemort at bay. For example, he could put a powerful protective charm on the place where Harry is staying.
It's possible that in the cave, they start to see each other as equals rather than just a mentor - student relationship. They might argue about the best way to deal with the cave's mysteries at first, but through that process, they learn to value each other's perspectives. Also, if one of them gets injured in the cave, the care and concern shown by the other would enhance their relationship.
It could potentially strain the relationship. If Sirius misinterprets the situation, it might create some tension. Harry and Hermione would feel like they need to explain themselves, and Sirius might be a bit standoffish until he gets the real story. For instance, if he thought they were hiding something from him, it could make things a bit rocky between them for a while.
It's also likely that they go to Romania. Given Sirius' knowledge of the wizarding world, he might know of a safe haven there. In Romania, they could be around dragons and learn about dragon - related magic. Harry would surely be fascinated by the dragons and it could be a place where he can grow stronger in a different kind of magical environment.
It may explore the emotional bond between them. Sirius could be like a father figure to Harry. He gives Harry advice and guidance, which is different from what Harry gets from others. This special connection makes Harry trust Sirius more than anyone else.
It could develop in a complex way. The spanking incident might initially create tension between them. Harry could be angry or resentful towards Sirius at first.
At first, it would probably be very tense. Harry would be suspicious of Voldemort's motives, and Voldemort would be cautious of Harry's potential to rebel. But as time goes on, they might develop a strange sort of understanding. Harry could start to see Voldemort as more than just a pure evil figure, and Voldemort might start to view Harry as something more than an enemy.
The relationship would become extremely complex. Harry would be confused and conflicted. He's been taught all his life that Voldemort is pure evil, but now he's been saved by him. Voldemort, on the other hand, might start to see Harry in a different light, perhaps as a tool or as someone with whom he can form an unusual bond. It would be a relationship full of mistrust on Harry's part and manipulative intentions on Voldemort's.