Yuki is the daughter of the Kuran family.
Kaname said that Yuki was the child born to become his wife.
In the Pureblood race, incest isnt uncommon.

Yuki was placed on a bed inside and she started to crave blood.
She looked older, maybe it was because of her vampire genes had returned causing her hair to be longer.
Kaname told her not to hold it (the craving) in, and she pushed him down on the bed and started sucking his blood and crying at the same time.
Kaname hugged her and told her that He held on to an anxious emotion, waiting for this day. ( I dont know how to correctly translate this sentence. It made sense in chinese though)

Yuki remembered her parents and became confused. Kaname hugged her from behind and calmed her down.
Yuki said that it is abnormal for her to like Kaname, her own brother.
But Kaname replied, "So? We are bethrothed"
You find out that their parents are also brothers and sisters.

Rima who found out that Shiki isnt Shiki, ambushed Ichijou and Rido.
She fought with Rido and got hurt in her abdomen.
Ichijou tried to help her, but he was stopped.
Rima yelled for Shiki to fight for his own body.
Shiki heard her and started trying to regain control.

Yuki smelled the scent of Rima's blood, but was relaxed that it wasnt Zero's blood.
Then she felt depressed bc she remembered the expression Zero had when he found out about her pureblood statues.
She went to in front Zero's room.
Yagari came back.

Kaname is just hiding the truth from Yuuki due to whatever reason. Yuuki doesn't know that Kaname is not her real brother, because she grew up thinking Kaname as her brother..but Kaname was probably adopted into the Kuran family before she was born. However, he is still a Kuran since kurans blood is flowing through his body, but not Yuuki's sibling. Yuuki was engaged to Kaname, because she was born to be his wife. And alternately, it was done so to keep their blood pure. Cha 36 was definately a hot chapter...I loved how Yuuki pushed Kaname down on to his bed and licked his neck and bit him. Then Kaname licked her tears or blood off her chin. soo hot

Yuuki also mentioned that she only desires Kanames blood. And later on she said "all this time..I've been in "love" with my brother"...KanaYuki anyone?