Yukiochimura ni Oujosama! is basically a crossover epilogue from 2 of Hiro Fujiwara-sensei's work that is Kaichou wa Maid-sama! and Yuki wa Jigoku ni Ochiru no Ka (Does Yuki Go to Hell).
If you try to read the plot or summary from the Wikia, there's a 100% chance that you'll be still confused. Why? Well, you might want to read the other manga if you want to know the whole story and get the emotional investment that Hiro-sensei put there. You're basically spoiling yourself for Yuki wa Jigoku ni Ochiru no Ka manga if you read the crossover first.
However, if you still want the explanation about the whole story of this special edition, you'll need a quick back story for the other manga:
The dude, the black-haired high-schooler one that speaks English also the newly transferred triplet's classmate you saw, he's Takaya. The 5 other people that you saw later in the chapter is his friends and the blond waitress is his girl. Long story short, the dude sacrificed himself for the sake of his village (the Mutsuji Village) and friends. He died 16 years ago. That dude was reborn again as an infant straight after his sacrifice. His memories are still intact and decide he's old enough to be with them again back at the village. That's the whole premise.
Meanwhile, we have Usui and Misaki's kids: Usui Sara and Usui Rui.
The story starts as the family of four went for a trip to Kyoto. Usui and Misaki albeit reluctant, let those chibis on their own while they're on a date with sort of a deal that Rui is constantly communicating with his parents.
Sara is restless. The girl hates mundane things, is a huge mystery geek and wished for something exciting happens instead (supposedly, Kyoto is a Japanese mystery shack in her eyes).
Then they stumble into 'Enma-kun's Lodge', a shop where the mascot of Mutsuji village resides in the city. There, they met the triplets. They see the triplets struggling with foreign visitors due to their lack of English speaking ability, and Sara lits up thinking she can do something interesting by helping them. Her moment, however, was stolen by Takaya. Yes, the Takaya (the formerly dead-dude Takaya).
Sara senses something is off with Takaya's vibe. Takaya decides to help the triplets with their 'Trip to Enma-kun's Hometown, a Day-trip to Mutsuji village' travel guide job. That's when Sara said "I finally find something interesting" and thus forcing Rui to embark on her mystery journey as both Holmes and Kindaichi towards the mysterious Mutsuji village.
After watching Takaya's interaction with the triplets' twin younger sisters, Sara confirms aloud to her brother that she does find Takaya's aura suspicious and sensing there are incidents in Mutsuji village, while her brother complained about her character inconsistencies.
Upon arriving, you'll find places that's an Easter egg for the other manga, as Sara sense Takaya's wistful aura while they're sightseeing. the group arrived at a cave (those Japanese creepy caves), and Sara's mystery senses went overboard, Takaya then said "I wonder... It's possible, isn't it? For there to be a corpse or two." (is both teasing Sara and subtly hinting manga trivia)
Takaya then ask about the roads which the triplets explain about villagers believes that there is a god living in the cave that protects Mutsuji. The triplets then wish them to have a break and stop by Mutsuji's famous local cafe, while Sara on the other hand, shamelessly address that Takaya has some sort of revenge plot, and try to interrogate him. Takaya bluntly said he has no means to play along with her plot and states that he's here simply to meet his girlfriend.
Sara is deflated and utterly discouraged by the revelation that her 'mystery journey' was in fact a mere romance or fantasy story. The triplets then after securing seats in the cafe by phone, proceed the group to the infamous cafe Mutsuji.