* When Ryoko tried to kill Kyon, that was outside of her mandate and her authorization. Such questions needed to at the very least be deferred to Yuki, unless Yuki was put out of commission, but Ryoko clearly did it on her own, concealing her plan from Yuki. When Yuki became aware of what Ryoko was doing, naturally she acted to prevent the unauthorized action from occurring (and she had her own motives).
* Basically, at the start, in Haruhi's 1st year in high school, Ryoko was assigned to be the interface who would have primary contact with Haruhi, but Yuki remained the brains of the operation and the agent in charge.
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