No, it's not appropriate at all. These kinds of stories are inappropriate for public discussion. They are private and personal matters that should be kept within the bounds of personal privacy, not something to be spread around in any form.
This situation is complex. You can also consider reaching out to a professional, like a family counselor. Explain the situation to them and get their advice on how to deal with it. They can provide you with strategies to set boundaries and deal with the emotional turmoil this has caused. They might say things like 'It's important to assert your boundaries and also understand if there are underlying issues in your mom's behavior that need to be addressed.'
Sharing a story like that is highly improper. It not only goes against moral norms but may also cause discomfort and harm to the people involved. In a civilized society, we should focus on positive, healthy and respectful topics.
This is a very difficult and inappropriate scenario. It could be that there is some misunderstanding or a serious issue with boundaries in your family. You may need to seek the help of another family member, like a grandparent or an aunt/uncle, who can mediate and help establish proper family dynamics. You could explain the situation to them and say 'I'm really uncomfortable because mom did this, and I don't know how to handle it.'
Since we only know that big sister watched a story, we can't be certain who was with her. She could have been in a public place like a library and watched the story with other people around, but not really interacting with them. Or she could have been at home with her pet, while the pet was just lying beside her during the story - not really 'watching' but still being there.
Perhaps it was a special occasion like a birthday or a holiday, and the mom was baking a cake. The girl watched intently, maybe to pick up some tips for her own baking in the future.
In this story, she might be in danger. Since she doesn't know she's being watched, someone could be plotting something bad against her, like stealing from her or causing her harm.
No, it's not okay. We should respect the idols. BTS members, including Jungkook, are public figures who are looked up to by many fans. Creating fanfic with inappropriate content like this goes against the basic respect and moral standards in the fan community.