I'll Save This Damn Family! is a Manga/Manhwa/Manhua in english language, Comedy series, english chapters have been translated and you can read them here. You are reading chapters on www.mgeko.nl fastest updating comic site. The Summary is

Ji-Woo Lee, an author gets reincarnated into her novel as Tara Elias, the 5th daughter of the Elias family. However, the family is supposed to fall soon, and everyone in it will be executed. Ji-Woo insists that she will escape her fate.
"I thought everything was going smoothly."
That is, until she meets the second prince. Prince Kyle Amur.