Here’s the thing. I think a lot of people see Elsa’s parents choice to shut her away from Anna as mostly Agnarr’s choice, especially in light of the fact that Iduna was friends with Gale as a child and that she comes from the Northaldra. But Grandpabbie makes it very clear to them that Elsa could be hurt for her powers and I think that’s something Iduna would have related to very heavily.

After all, she wasn’t exactly screaming the fact that she was Northaldran around to the world after King Ragnar died and at the scene where Grandpabbie warned them, she hasn’t even told Agnarr yet. Iduna hears his warning and knows exactly what he means because that’s what she choose for herself. She’s taken that part of her and locked it away from Agnarr and no doubt felt that Elsa could do the same. After all, they’re shown to love each other, they have a genuine connection without Agnarr knowing about that part of her. She had every reason to expect that Elsa would be able to learn to control her powers (that up until that day were very well controlled!) and still form genuine and meaningful relationships and have a happy loving life.

Agnarr has been raised since birth to be the king. He doesn’t really understand magic, especially since his only experience with it resulted in his fathers death and the disappearance of many men, but he does understand putting on a brave face and doing what needs to be done. He understands responsibility. He was 14 when his father died but after all, he’s not asking Elsa to be Queen, he’s asking her to hide her previously well controlled powers.

They both had every reason to relate to and expect Elsa to be able to hide her powers. The life of royalty after all, comes filled with expectations and responsibilities and Elsa has shown herself to have good control so far. In every scene after The Accident they’re shown together and neither seemed to have any doubt about their choice to listen to Grandpabbie. I’d even argue that Elsa did gain control over her powers. After all, every F1 scene with involuntary magic after age 12 or so is one where Elsa is incredibly upset. She’s out of her room to say goodbye to her parents before their voyage and presumably eats dinner, has her studies, etc. Her parents left to find the source of her powers in hopes that they could make her happier, hate her powers less, but they did so knowing she would be okay while they were gone. She loses control when she can’t calm down enough to go to their funeral yes, but even the Coronation? An incredibly stressful and terrifying even that Elsa has been dreading for years? The slightest bit of frost during the swearing in and that’s all, until Anna has a big screaming confrontation with her while announcing she’s engaged. She did learn to hide her powers, and she did so very well until she argued with Anna, got chased out of her own castle, and subsequently decided she was gonna embrace her powers.

I genuinely believe they knew she was unhappy but had no idea how deeply she had internalized their messages, how much she hated herself because after all, she can’t control her powers when talking about emotional subjects and “hey mom and dad you make me feel like I’m an awful person for being born the way I was” is the exact kind of thing Elsa would never talk to them about for fear of losing control and hurting them. Physically and emotionally, since she knows they only did it to protect her. And up until they died, she never let them touch her but she still seemed to be pretty close to her parents. She wasn’t entirely alone, not until she died and things went from “I miss my sister and hate myself but have my parents love and guidance” to “there’s not a single person who can help or love me and I have the responsibility of a kingdom.” They never knew how badly she was hurt to make them think that the safety it brought Elsa wasn’t worth the cost of keeping it a secret. I think Iduna and Agnarr both viewed their choice as worth it and felt they did the right thing, even if they were not yet confident enough in Elsa’s safety to open the palace up again. I’m sure they thought making her pretend less was a kindness to her, to let her be herself at least in her own room.