There should not be an 'erotic' story involving Batman's mother Martha Wayne in the proper context of the Batman franchise. Batman stories are mainly about crime - fighting, justice, and the hero's journey. Any such inappropriate content goes against the essence and values of the Batman lore.
In many fanfictions, Jason saving Batman in 'Batman Arkham Knight' often shows a new side of their complex relationship. It could be a moment of redemption for Jason. Maybe he realizes the true meaning of Batman's mission and decides to put aside their differences. This scenario allows for deep character exploration.
One proper story is the origin story of Batman. Martha Wayne was Bruce Wayne's mother. They were a loving family until the tragic event of their murder in Crime Alley. This event was the catalyst for Bruce Wayne to become Batman, driven by a desire for justice. It's a story of loss and the birth of a hero.
Yes, in the Batman lore, there are many proper stories about Batman and his mother Martha Wayne. These stories usually focus on her death as a catalyst for Bruce Wayne's journey to become Batman, and how her memory and the values she instilled in him shape his actions as the Dark Knight.
I haven't read the 'Martha Martha' short story specifically. But generally, when analyzing a short story, we can start from aspects like the characters. Maybe Martha is the main character and we can look at her personality traits, her goals and desires. Another aspect could be the plot. Is it a linear plot or does it have flashbacks? For example, if it's about Martha's journey, whether it has a clear beginning, middle and end in terms of her experiences.
In the fanfic, the Teen Titans could be in a situation where they are being mind - controlled. Batman, with his strong will and training in resisting mind - control himself, could break the control on the Titans. He might use a combination of technology and his own mental discipline. For instance, he could use a device that emits a frequency disrupting the mind - control signal. Then, he would protect the Titans from the villains who were controlling them until they fully recover.
One positive aspect is the emotional connection. Martha's love for Bruce was unconditional, and this love became a driving force for Bruce. Even after her death, it was that love that made him want to protect others in Gotham.
One possible plotline could be that Jason has been captured by a new and dangerous villain in Gotham. Batman uses his detective skills to track Jason down. He then has to fight through a horde of henchmen to reach Jason. Once he does, he has to deal with some sort of trap set by the villain to keep them from escaping easily.
Perhaps in the 'Martha Martha' short story, there are events related to Martha's relationships. Maybe she meets a new person who has a big impact on her life, like a new friend or a love interest. This could lead to a series of events such as going on adventures together or having conflicts because of different opinions.