He could be brought in as a sort of reluctant ally. For example, the Young Justice team is facing a new type of enemy that has some similarities to the demons Inuyasha is used to fighting. They track him down and convince him to help them out, even though he's not too keen on working with a bunch of 'strange' heroes at first.
One way could be by having Inuyasha be from a different dimension that somehow gets connected to the Young Justice world. Maybe a magical portal opens up and he stumbles through, bringing his own set of problems and abilities with him.
Well, it could be that the writer is a big Inuyasha fan and wanted to incorporate that character into the Young Justice universe for a unique crossover. Maybe they thought Inuyasha's abilities, like his swordsmanship and demon powers, would add an interesting dynamic to the Young Justice story that Kagome's skills might not.
Well, in a Young Justice fanfiction, the concept of Naruto being immortal could be integrated in various ways. One way could be through some sort of magical or scientific experiment gone wrong that gives him immortality. Maybe it's a meta - human experiment in the Young Justice universe that accidentally gives Naruto the same powers as Vandal Savage, including immortality. Another possibility is that it could be a result of a powerful jutsu he uses that has unforeseen consequences and makes him immortal.
One idea could be to have Inuyasha end up in the Young Justice universe through some sort of magical portal mishap. He could initially be seen as a threat due to his demon nature and his sword, Tessaiga. But then the Young Justice team realizes he's more of a lost soul and they try to help him get back home while also dealing with villains who want to use Inuyasha's power for their own gain.
Another possibility is that he could be a part of a multi - dimensional or time - travel plot. Maybe he gets pulled into the Young Justice universe due to some interdimensional rift. His presence could then create a whole new set of storylines, like the team having to deal with the villains that follow him through the rift, or him having to adjust to the different rules and politics of the Young Justice world.
In fanfiction, their romance can be very intense. Writers often show Inuyasha being more protective of Kagome. For example, he might fight off stronger demons to keep her safe. This portrayal emphasizes his deep love for her and his willingness to risk everything for her well - being.
Well, in some fanfictions, Kagome might hurt Inuyasha by saying mean things. For example, she could bring up his past mistakes or insecurities in a cruel way during an argument. This could really wound his pride and his feelings towards her.
Kagome would probably be shocked at first. Then she would start yelling at Inuyasha, demanding to know why he's doing this. She's not the type to just sit there and take it.
Well, in some fanfictions, Inuyasha might hurt Kagome's feelings by being overly possessive. For example, he could get jealous when Kagome talks to other male characters and then say something harsh. Another way could be that he doesn't trust Kagome's judgment at times, like when she tries to come up with a plan to deal with a demon and he dismisses it rudely, making her feel unappreciated.
Inuyasha is devastated when Kagome gets hurt. He blames himself, especially if he was supposed to be protecting her. He'll pick her up gently and try to find a safe place to tend to her wounds. He might also call for help from his friends like Miroku or Sango. He'll stay by her side until she recovers, constantly on guard against any further threats.
Some great Inuyasha and Kagome fanfictions include those that focus on their adventures after the end of the series. For example, 'A New Beginning' which shows them building their life together in the feudal era. It has really good character development and stays true to their personalities.