SOLVED. YA Fantasy - Time Travel. Main character discovers she has the family curse of jumping to the past instead of her cousin. [s]

[Lala~]

I remember main character's family had some kind or family curse/tradition that someone born a certain day and time will have an ability to time travel to the past, and they prepare for it beforehand. MC's cousin was supposed to be the one, so she is taught mannerisms of the past century, playing music instruments I think, ball dancing and etc. But then turns out it was the MC who had the curse because her birth date was wrong, and she was unprepared for it all. She comes back and they start training her, and there was also another guy who time travels to the past. I don't remember much of other details, but I think a villain in the past turned out to be her teacher in the present.

Thank you in advance!

[SamSpayedPI]

Ruby Red for Emilie's link.

[Lala~]

Ruby Red is the one, thank you Emilie!