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Okay, if you're curious. I don't remember there being any "twist" about Sheryl being adopted, so we probably dodged that, and her family is just trash. (I mostly just remember being dumbfounded that MATCHES ended up being so important to the plot.)
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Anyways. Ending Spoilers, I guess.
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So the new matches are safely invented, and Hyland insists on the patent being placed under Sheryl's name. But her dad protests and tries to get the patent under HIS name, because of his match business. Sheryl doesn't know what to do about it, so they decide to do nothing for now.
The king invites Sheryl and Hyland to a party so he can meet "the Jewel Princess," and her family is also invited. Meryl and the mother protest to the king that Sheryl stole the king's letter and pretended to be Meryl to marry Hyland (which is treason), but Hyland brings in the old carriage driver as a witness to prove that the family were complicit in the crime. The family is horrified and tries to get out of the situation, and pretend that "the Jewel Princess" was Sheryl after all.
So the king gives the family a choice, asking if they sent Sheryl to marry Hyland (in spite of the royal order), or if they interrupted his party to lie to him (by bringing up this story and then saying that it wasn't true). Both choices would be considered treason and would be punishable by law.
Sheryl decides that now is a perfect time to ask her father what he planned to do by taking her patent for the new and improved matches, and he tells her that he doesn't intend to do anything with it--he just wants that patent to insure that the "safe" matches never get made and he can keep his monopoly. Which serves as a wakeup call to Sheryl, and she immediately disowns her family, because they never loved her.
And so the king punishes her family, but assures Sheryl that he won't blame her, because in his eyes, Sheryl really is "the Jewel Princess."
So I was curious and read the novel this manga was based on. It's pretty short, less than twenty chapters. So as far as character growth goes, Cheryl (the female lead) has barely started her healing journey by the time the novel closes.
Which means that the manga basically HAS to add scenes like the kitchen fire, because "My father is pushing matches as a business product to a ridiculous degree, despite its inherit dangers" only comes up as dialogue TWICE in the novel itself.
I don't know that I actually like the change, but as I said before, it's a short novel. They clearly had to do something. ╮( ̄▽ ̄)╭