I'm not sure specifically as 'unseemly' is a rather broad term. It could potentially be about a lady who behaves in a way that is considered improper according to the social norms of the story's setting. Maybe she challenges the traditional roles or values in the society depicted in the novel.
People who like stories about complex female characters might be interested. Those who enjoy exploring the boundaries of social norms through literature could also be drawn to it.
For truth, we can ask family members 'What's the most embarrassing but funny thing that happened to you at a family gathering?' For dare, 'Draw a family portrait in 5 minutes.' These are simple and clean ways to play truth or dare in a family, without any inappropriate elements.
Snape might be initially in shock. He had trusted Lily deeply, so the betrayal would hit him hard. He could become very angry and bitter, perhaps vowing revenge against her. He might also close himself off emotionally, not wanting to trust anyone again.
He might be initially shocked. After all, getting a Howler is a very public and embarrassing thing. He could be so ashamed that he immediately hides away to read it privately, his face turning red with a mix of anger and humiliation.
Harry would be heartbroken. He'd likely first try to jog their memories in simple ways, like showing them things that were important to their family. He might be in denial at first, thinking it's just a temporary thing.
Perhaps the perception of her 'unseemly' behavior is due to misunderstandings. It could be that she is trying to fit in a new social circle and is overdoing it. For instance, if she is new to a group that has a more liberal style, she might be adjusting in the wrong way. The key is to communicate clearly with her about what is acceptable and what isn't.
There are versions where Snape reacts defensively. Let's say Lily confronts him about his actions that seem to be harming her or her friends. He would immediately start justifying himself, listing all the reasons why he did what he did, trying to make Lily see his point of view, even if deep down he knows he might be in the wrong.