There was no real Elsa and Hans love story. What went wrong was that Hans was a liar. He was only after the throne of Arendelle. He deceived Anna and there was never any intention of having a relationship with Elsa.
In the so - called Elsa and Hans love story, everything went wrong because it was based on false pretenses. Hans was self - serving and had no real feelings for anyone in Arendelle, least of all Elsa. Elsa was preoccupied with her own issues like controlling her powers and protecting her sister. There was no foundation for a love story as Hans was only interested in his own gain, and his actions of betrayal towards Anna showed that he was not capable of any real love, especially not with Elsa.
The idea of an Elsa and Hans love story is a false one. In the Frozen universe, Elsa is a complex character dealing with her own insecurities and the power she has. Hans is a conniving man who wants to take over Arendelle. He fools Anna into thinking he loves her, but there's no relationship with Elsa. Elsa is more concerned with her family and her place in the world, and any thought of a relationship with Hans is completely out of the question as his true nature is revealed to be quite malicious.
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.
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.
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.
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.
One possible plot could be that Elsa and Hans meet secretly. They start to share their true feelings and dreams away from the prying eyes of the kingdom. As they fall deeper in love, they face the challenge of how to make their relationship acceptable to the people who have misjudged Hans in the past.
One popular Elsa and Hans love fanfiction is 'A Different Beginning' which explores what could have happened if Hans had truly reformed and he and Elsa developed a relationship in a more positive way. Another is 'Frozen Hearts Reunited' where they meet again after the events of the movie and gradually fall in love through various challenges they face together.
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.
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.
One possible story could be that after many trials and reconciliations, Hans and Elsa find a common ground. They might start off as enemies, but over time, they come to understand each other. Elsa's ice powers could play an interesting role in the pregnancy, like creating a special, safe environment for the baby. And Hans could change his ways, becoming a more loving and protective partner and father.