It could be shown as a very strained relationship. For example, Wonder Woman might initially be very hostile towards Batman, seeing him as a threat to the order Superman has created. But as time goes on, she starts to see the value in his approach. There could be many tense confrontations between them that gradually turn into more respectful exchanges as they understand each other better.
Another way to portray their relationship is as reluctant allies. They don't trust each other fully at first. But they realize that they need each other to achieve their own goals. So they start working together in a very cautious way. For instance, they might exchange information in a very guarded manner at the beginning and then slowly build more trust as they see the positive results of their cooperation.
Often, they're shown as equals. Batman respects Wonder Woman's power and her moral compass, and she admires his intelligence and determination. In some fanfiction, they share a bond that goes beyond just being teammates in the Justice League.
In an Injustice fanfiction, their relationship might develop through conflict at first. They have different views on how to handle the chaos in the world. However, as they face greater threats together, they begin to understand each other better. For example, when they are up against a powerful new villain that neither could defeat alone. This shared experience could lead to a stronger bond between them, evolving from grudging allies to close friends or even something more romantic depending on how the story unfolds.
Their relationship could be shown as a very professional partnership. They respect each other's skills and intelligence. Batman admires Wonder Woman's strength and her connection to the mythological world, while Wonder Woman respects Batman's detective skills and his determination to protect Gotham.
Their relationship could be portrayed as a mentor - mentee relationship. Catwoman, with her years of experience, could be teaching Batman Beyond some of the more subtle aspects of crime - fighting, like how to read a criminal's motives just by observing their body language. Another way is to show them as rivals in a different sense. Instead of just fighting over loot, they could be competing to solve a mystery first. Or, they could be portrayed as reluctant allies. They don't trust each other completely, but they know that they need to work together to stop a greater evil.
At first, it might be a bit rocky. Batman is used to working alone and being in control, and Wonder Woman is a powerful and independent hero. But as they face challenges together, they would start to respect each other's abilities. They could develop a friendship based on mutual admiration for their different skills.
After the proposal, their relationship would likely become more public. They would no longer be just comrades in arms but an engaged couple. Their interactions would be more affectionate and they would start planning a future together.
To realistically portray their jealousy, it could be related to their insecurities. Batman might be jealous of Wonder Woman's god - like status and the respect she gets from others because deep down he feels inadequate without his gadgets. Wonder Woman could be jealous of Batman's strategic mind and the way he's able to solve complex problems so quickly. This jealousy could manifest in how they interact with the other Justice League members. For instance, Batman might be overly critical of Wonder Woman's decisions in front of the others, and Wonder Woman might undermine Batman's authority subtly. It's all about showing the human (or superhuman) emotions beneath the capes and tiaras.
It would be a very unique relationship. Batman would be the more cautious and protective parent, always worried about her safety given his own experiences. Wonder Woman would be the one to encourage her to embrace her powers and use them for good. Their daughter would look up to both of them, learning from Batman's intelligence and Wonder Woman's strength.
Their relationship could be portrayed as a more mentor - mentee relationship. Batman could see the potential in Harleen to be redeemed and takes her under his wing, teaching her how to use her skills for good instead of for the Joker.
One idea could be that Batman and Wonder Woman have a major disagreement over how to deal with the Injustice regime. Batman wants to use more stealth and subterfuge while Wonder Woman believes in a more direct approach. This could lead to some intense battles between them, not physical but more of a battle of wits and ideologies.