One scenario in the fanfiction could be that Batman gets jealous when he sees Catwoman flirting with a rich businessman during one of her heists. He might start to question her motives and their relationship. This jealousy could cause him to act out of character, perhaps being more aggressive or possessive towards Catwoman than he normally would be. And Catwoman, being the independent character she is, would not take kindly to this sudden change in Batman's behavior, leading to a rift between them that would be interesting to explore in the story.
A way to develop their relationship in this type of fanfiction is through joint parenting. They might have different approaches to raising their kids. Batman could be very strict about discipline and training, while Catwoman might be more lenient and focus on teaching the kids about the importance of freedom. Through these differences, they learn to understand each other better and grow closer as a couple. Also, they could face external threats to their family which forces them to rely on each other more, strengthening their bond.
She might be very surprised at first. After all, Batman is not one to show his emotions so openly. But then she would likely be overjoyed. She has deep feelings for Batman too, and this proposal would be a confirmation of their complex relationship.
Well, it is indeed a classic. Catwoman and Batman's love story is not your typical love story. They come from different worlds. Batman is the Dark Knight, dedicated to justice, while Catwoman is a cat burglar. But their attraction to each other is undeniable. Their love is often a struggle, as they have to deal with their own moral compasses and the expectations of Gotham. This makes their love story one of the most interesting and enduring in the Batman franchise.
The Penguin often makes an appearance. He can add an extra layer of chaos and villainy to the story. His devious plans can either get in the way of Batman and Catwoman's relationship or be a catalyst for them to work together more closely.