At first, Harley would probably be very confused. Batman has always been on the opposite side from her. But after being saved, she might develop a grudging respect for him. This could gradually turn into a sort of friendship where they exchange information about the criminal underworld. Batman might also start to see Harley as more than just a villain, as someone who was a victim of the Joker's manipulation and is now trying to find her own way, and their relationship could become one of mutual understanding and cooperation.
Their relationship would likely become more complex. Harley might start to trust Batman more. Instead of seeing him as just another authority figure to rebel against, she could view him as a protector. This new - found trust could lead to her being more open to his ideas about reforming and leaving her life of crime behind.
The relationship might become more complex. Harley would likely be more protective and demand more stability from the Joker for the sake of the baby.
Batman's character could be developed by showing his compassion. Usually seen as a brooding and dark figure, saving Harley Quinn could highlight his ability to see the good in people, even someone as chaotic as her. It could also show his adaptability, as dealing with Harley is different from his usual foes. He might have to use more psychological tactics rather than just brute force.
Their relationship would become more complex. Batman might start to see the Joker in a different light, perhaps as a victim of his own madness rather than just a pure villain. The Joker, on the other hand, might be confused by Batman's act of saving him and could develop a strange respect for Batman, or he might try to use it to his advantage in some new, devious plan.
Gotham's perception of Batman could change. Some might see him as being weak for getting involved with a former villain like Harley Quinn. This could lead to a loss of some of the public's trust in Batman. However, if Harley truly reformed and they worked together to make Gotham better, it could also inspire hope among the citizens. They could see that even someone like Harley can change for the better, and that love can conquer even the darkest of pasts.
To develop their relationship in fanfiction, Harley Quinn could start by making small acts of kindness towards Batman. Maybe she leaves him anonymous tips about Joker's plans. Batman, being observant, would start to wonder about her motives. Then, they could have chance encounters where they have to work together briefly. As time goes on, Harley could gradually distance herself from the Joker's influence. Batman could offer her a chance at redemption. Their relationship could also be developed through mutual respect for each other's skills. Harley Quinn is a skilled fighter and Batman could come to recognize that. In turn, Harley could admire Batman's detective skills and his unwavering sense of justice.
Their relationship could potentially soften on Joker's part. Having a baby might make him see things in a different light. He might not be as cruel or reckless as before, at least when it comes to the baby. Harley, on the other hand, would be more determined than ever to keep the family together, even if it means constantly trying to reform the Joker. But at the same time, the pressure of raising a child could also lead to more fights between them as they struggle with their own issues and new responsibilities.
In certain fanfiction scenarios, Harley Quinn may also help Batman on an emotional level. She could understand the Joker's twisted mind better than most. By sharing her insights into what makes the Joker tick, she could help Batman anticipate the Joker's next move. For example, she might explain how the Joker's need for chaos and attention drives his actions, which would give Batman an edge in trying to stop the Joker's evil plans.
Their relationship could become more trusting. Since Batman saves Wonder Woman, she might start to see him as more than just a brooding vigilante. She could open up more to him and share her fears and secrets.
She would likely become more vengeful. Losing her baby is a huge blow, and Harley Quinn, known for her wild and impulsive nature, would want to seek revenge on whoever or whatever was responsible.
In some fanfictions, their relationship starts as pure enmity. Batman is constantly trying to stop Poison Ivy and Harley Quinn's criminal activities. But as the story progresses, they might find common ground. For example, they all might have a shared enemy that forces them to work together briefly.