Is a girl considered a seductress or a spy if she conveys to her father a conversation she overheard between her brother and his wife about her parents, intending to embarrass them so they would stop doing that, knowing that her intention was pure?

You committed two forbidden acts: The first is listening to someone whose speech you dislike listening to, for which the Prophet, peace and blessings be upon him, threatened that molten lead would be poured into the ears of anyone who does so on the Day of Resurrection. The second is backbiting (namimah), as you conveyed your brother's words to your parents, which ruined their relationship. You should not have listened to them. If their words reached you without you eavesdropping, then it was obligatory for you to advise them and remind them that Allah is aware of their actions, and to remind your brother about disrespecting parents (uquq al-walidayn). Your obligation now is to repent.