The thing that bothers me most about this is that if it is a game, there could be other capture targets the heroine could be going after, it doesn't necessarily have to be the prince. And there would also be bad ends where the heroine just "plays badly" and loses. She just assumed with no evidence the worst possible case for herself. Her trying to push the two together actually ends up making her look as an actual villainess, in that she ends up humiliating the heroine over and over in her attempts to get the two together.
The heroine meanwhile appears to be a decent person, not some mean reincarnator type. The only somewhat sus thing she did was ask the prince for a dance, in front of his fiancee even. It could somewhat be explained if she didn't know proper ettiquette from how she grew up. It's specially odd because she's clearly so bad at dancing. Did she not know she was a terrible dancer?