If such a fanfiction exists, perhaps the motive could be a misdirected attempt at protecting the greater good. Maybe Dumbledore thought Hermione's parents were in some way a threat to the wizarding world's secrets that he was trying so hard to protect. But this is still a very far - fetched idea as Dumbledore was always about protecting life in the official story.
One possible motive could be that Dumbledore saw a future where Harry's parents' deaths were necessary for a greater good. Maybe he knew that Harry would be the only one to defeat Voldemort in the end, and their deaths were a catalyst to set Harry on that path.
I'm not sure if there is such a specific fanfiction. However, in the original 'Harry Potter' canon, Dumbledore would never do such a thing. Fanfictions sometimes take wild and unorthodox turns, but this would be a very dark and out - of - character concept. It might be a very rare and edgy take in some extreme fan - created stories.
Yes, there are likely fanfictions out there with this dark and alternative take. Fanfiction often explores non - canonical ideas, and this would be a very radical one. It goes against the established lore in the official 'Harry Potter' series, but that's the nature of fanfiction - to play with different concepts.
It could also be that Dumbledore has some secrets that he's afraid Hermione will uncover if she's left to her own devices. Hermione is known for her inquisitive nature. So, to keep these secrets hidden, he attempts to control her. For instance, if there are some hidden aspects of Hogwarts' history or certain faculty members that he doesn't want exposed, he might use control over Hermione to prevent her from delving too deep.
Dumbledore might be motivated by his over - arching plan to defeat Voldemort. He could see Hermione as a sacrifice that needs to be made. Maybe he believes that by betraying her, he can gain some crucial information from the enemy that will ultimately lead to Voldemort's downfall.
It could be a revenge plot gone too far. Suppose her parents did something in the past that she just found out about, and in her new dark persona, she decides to take the ultimate revenge. Or perhaps she has fallen so deep into the dark side that she no longer values family and sees them as just another obstacle in her path of darkness.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
Well, it could be for the sake of exploring a different kind of magic or a different set of rules in the wizarding world. Perhaps in this fanfiction's version, the parents were under some sort of dark magic influence that made them turn on Harry. Or it could be a psychological exploration. The writer might be interested in delving into the minds of Harry's parents and seeing what could make them do such a heinous act. It could also be just a very different take on the concept of family and love in the 'Harry Potter' universe.
One possible motive could be jealousy. Grindelwald might be jealous of Dumbledore's power and popularity in the wizarding world. By kidnapping him, he wants to prove that he is the more powerful one.
Well, in some fanfictions, Harry might attack Dumbledore if he discovers that Dumbledore has been using him as a pawn in a bigger game all along. This feeling of betrayal could drive him to lash out. Also, if there is a prophecy that he misinterprets to mean Dumbledore is a threat to his future or the future of his friends, that could be a motive.