Working!!/WMG

Kyouko actually loves Yachiyo back

Judging by her emotionally stunted behavior, Kyouko likely has trouble showing her true feelings in general, so showing affection for Kyouko would be rather tough for her. Her only outlet is to have Yachiyo prepare food for her so she can hand out compliments.
The main reason Kyouko (mostly) gave up her delinquent life style could even be that she could be with Yachiyo at the restaurant.
Of course, her outcry of "Yachiyo is mine" should be as a rare indication about how she really feels.
And Yachiyo herself might be aware of Kyouko's feelings, but knows she can't push the issue. Poor girl--she didn't find the easiest person to fall for.
Furthermore, in the manga, volume 10, when she learns Satou's in love with Yachiyo she, unconsciously, takes a nailed bat and is seriously disturbed.

Since she knows that rebuffing Yachiyo can only end badly, she keeps up the charade to keep a hard worker and her belly full. Notice how she gets tired of Outo's treats just in time to save his life and says just the right words to keep her from killing him after Yamada's little Replacement Goldfish stunt.

She speaks very formally. Seems a little confused about how to do simple house hold chores when she first came. She became completely enamored with a girl who carries a katana more or less on sight. She knows how to plant bugs and making convincing cover for people. Just seems like stuff that might have been taught a little Yakuza girl.
- In fact, in the last chapters, Yamada's family has appeared in the manga. Her mother is a secretary and work with Takanashi's older sister's ex-husband. Her dad's passed away.