Well, perhaps Hiccup would be really nervous when meeting Elsa's parents. He might show them his dragon - riding skills to prove he's worthy. Maybe they would initially be skeptical of him because he comes from a different world with dragons, but then come to see his good heart.
Hiccup is the protagonist who embarks on the meeting with Elsa's parents. He's brave and curious. Elsa's parents, on the other hand, are the ones he's meeting. They are likely to have certain expectations and reactions. There may also be other secondary characters from either the How to Train Your Dragon or Frozen universes that could make an appearance and influence the encounter between Hiccup and Elsa's parents in the fanfiction.
Their relationship might start with curiosity. Hiccup would be curious about Elsa's ice powers and Elsa about Hiccup's connection to dragons. As they interact more, they start to respect each other's abilities and personalities. This mutual respect turns into friendship, and then gradually into love. The news of the baby would strengthen their bond as they now have a shared future to look forward to. They would support each other more, with Hiccup protecting Elsa during her pregnancy and Elsa using her powers to help Hiccup in his adventures.
Stitch could be accidentally teleported to Arendelle. Elsa, thinking he's a threat at first, freezes him. But then she realizes he's harmless. They then become friends and Stitch shows Elsa how to have more fun. He teaches her some of his crazy alien moves and Elsa in turn shows Stitch the beauty of her ice - made creations.
One possible antagonist could be a jealous sorcerer. He might be envious of Hiccup and Elsa's relationship and the power that their unborn child is said to possess. So he tries to harm Elsa during her pregnancy to stop the child from being born. Another could be some of the traditionalists from their respective kingdoms. They don't approve of their relationship and see the pregnancy as a threat to their old ways. They might try to separate Hiccup and Elsa, which would put Elsa's pregnancy at risk.
One possible plot could be that Hiccup, while on a journey with Toothless, somehow gets transported to Elsa's world. He stumbles upon Elsa as she is trying to control her powers in a difficult situation. Hiccup, with his experience dealing with dragons, offers her a different perspective on handling her powers. They gradually grow closer as they share their stories and in a moment of deep connection, they share a kiss.
In a fanfiction where Kaz meets Inej's parents, it could be a very tense and interesting scenario. Kaz, with his complex personality and past, might be quite nervous. He would probably try to put on his best behavior, but his natural wariness would still show. Inej's parents, on the other hand, would likely be very protective of their daughter. They might be initially suspicious of Kaz due to his reputation in the criminal underworld. However, if they see how he cares for Inej in his own way, they could gradually warm up to him.
Sure, there are numerous Jack meets Elsa fanfictions. In some, their encounter is a bit more of a friendly rivalry at first. Maybe they compete in a snow - building contest or something similar, and as they get to know each other better, they become friends and learn from each other's abilities and experiences.
In some Dramione fanfictions where Draco meets Hermione's parents, it can be quite an interesting scenario. Maybe Draco is initially nervous. He tries to make a good impression on Hermione's Muggle parents. He might show them that he's not the same as the prejudiced pure - blood wizard he once was.
Hiccup is adventurous and curious. He would be intrigued by Elsa's ice powers and her reserved nature. Elsa, on the other hand, is cautious and has been through a lot with her powers. Hiccup's boldness might initially make her a bit uncomfortable, but his kindness would draw her in.