Sister, In This Life I’ll Send You to Your Death

Spoiler. I’ve gone s few chapters in and it’s a very weak premise. People were very superstitious in the past the regressor could simply say she had a premonition of the things she actually lived through and the family would very likely have believed her. It would be far too much of a coincidence for her to have predicted that young woman turning up exactly when she did after the MC warned the family that the girl would turn up. She could have even given a description of the girl.
Additionally, even if her father did take responsibility for her, there’s no way that she would be given the privileges of her legitimate sister. They know nothing of her past or upbringing she can’t verify that she was protected or innocent. They can’t present her as a daughter of the house in the same way because they can’t offer her as a bride. Asian cultures were often more openly accepting of adultery but an illegitimate child, especially a daughter, would not be welcomed the way this girl is. Frankly as a daughter she would have no value in that sense. They might immediately farm an emotional attachment but couldn’t do present as socially acceptable.
They can’t prove her background or character. Just because she’s polite doesn’t mean she was well brought up. For all they know she could have been a prostitute, or thief or already be married. Even the evidence that she gives to prove she’s the prime minister’s child is very feeble. I find it hard to believe that it would be so readily accepted as sufficient proof along with the fact that she just happens to resemble the prime minister, frankly I don’t think she does look much like him, not the way she’s been drawn.
The sachet is something that someone other the woman he had an affair with could have easily obtained. And a girl that looks like him doesn’t mean anything either, people can resemble other people and have no familial connection to them whatsoever. And this was known in the past, it’s not just modern knowledge.
It’s much more believable if it was a son. Son’s had more value. A supposed illegitimate ‘son’ whose parentage cannot be 100% certain, wouldn’t be accepted as an heir but he could be a protector of the family. An adult ‘daughter’ would at the most be made a maid servant or be provided with a settlement and the possible option of a family retainer marrying her.