Anna would be a likely candidate to rescue Elsa. She loves her sister deeply and has shown great courage in the past. She would stop at nothing to find and free Elsa from Hans.
Well, one possible plot could be that Hans has some hidden motives for kidnapping Elsa. Maybe he wants to use her powers for his own gain, like ruling Arendelle through her magic. He could hold her in a secret location and try to force her to cooperate.
Their relationship would likely become more solid. Having a baby together means they have a new shared responsibility. They would have to rely on each other more, like when taking care of the baby at night or making important decisions about the baby's future.
It might start with a chance encounter. They see each other in a new light and gradually start to develop feelings. Their relationship develops as they exchange kind words and small gestures of kindness.
Anna could be the one to save Elsa. After all, she has proven herself brave and determined in the original story. She would stop at nothing to rescue her sister from Hans's clutches.
In Elsa and Hans love fanfiction, often there is a lot of character development. Since their initial relationship in the movie was so rocky, the fanfictions usually focus on how they overcome those initial negative impressions. For example, Hans might be written as having a change of heart more thoroughly and Elsa learning to trust again.
One possible plot in this fanfiction is that Hans kidnaps Elsa not just for power or revenge, but because he is being controlled by some dark magic. He takes Elsa to a remote location where she has to fight not only Hans but also the source of the dark magic to free herself and save Arendelle. Along the way, Elsa might discover new aspects of her powers that she didn't know before.
One key element is the exploration of their relationship. Since in the original story their relationship is quite complex, fanfiction often dives deeper into how they might interact on a more personal and romantic level.
One common theme is redemption. Since Hans was initially the villain, a lot of fanfictions focus on him redeeming himself in Elsa's eyes and winning her love. Another theme is the power of love to change people. For example, Elsa, who was so closed off, might open up because of her love for Hans.
Perhaps in the fanfiction, Elsa realizes that Hans was misunderstood. He was under pressure from his own family to try and take over Arendelle in a wrong way. As Elsa forgives him and they start working together to improve relations between their kingdoms, they develop feelings for each other. Hans courts Elsa in the traditional way, with flowers, poems, and horse - drawn carriage rides. Eventually, they get married and use their combined leadership skills to create a more prosperous and peaceful world for their people.