It can symbolize protection. Batman is the mentor, and when he carries Nightwing, it shows his instinct to keep Nightwing safe from harm, whether it's physical harm from villains or other threats.
In Lego Batman 2 set in Lego Gotham City, the story revolves around Batman's efforts to keep the city safe. He teams up with Robin and other heroes. They have to deal with the likes of The Joker and his devious plans. There are also side stories involving the other characters in Gotham, and the whole thing is filled with the charm of Lego building and play. For example, there are parts where they have to use Lego gadgets to solve problems and progress through the story.
One possible fanfic could involve a battle against a powerful villain. Nightwing might get injured while trying to protect Gotham. Batman then has to step in not only to defeat the villain but also to take care of Nightwing. He could use his advanced medical knowledge and resources in the Batcave to nurse Nightwing back to health.
The story length of Lego Batman 3 varies depending on how quickly you progress and explore all the elements. But on average, it can take several hours to complete the main story.
I would recommend 'Nightwing's Ascent'. This fanfic is amazing as it focuses on Nightwing's growth while still maintaining his connection with Batman. It has some really cool action scenes and emotional moments that make it a great read.
It's possible that such fanfiction exists. In the world of fanfiction, creators often experiment with different character dynamics. But in the traditional Batman and Nightwing relationship, Batman is more of a guiding figure to Nightwing. The idea of Batman being abusive is a deviation from the norm. It might be a way for some writers to add drama or explore the psychological impact on Nightwing if such a situation were to occur, but it's not in line with the general perception of their relationship.
In this fanfiction, often there's a power struggle. Nightwing, with his own set of skills and experiences independent from Batman, might oppose Batman on certain principles. Maybe it's about different approaches to crime - fighting. Nightwing could be more lenient while Batman is strict.
The Lego setting makes their relationship more light - hearted in a way. The blocky, colorful world of Lego gives a different tone to their interactions. For example, the physical comedy that can come from their Lego forms adds a new layer. Batman's cape might get stuck on a Lego piece while chasing the Joker, which can create a humorous moment that changes the dynamic a bit.