[Being the jerk sibling yourself makes one understanding Oookay, that makes warning bells go off in her head. Possessive? Just protective?]
...Thank you for the vote of confidence. [Still in the same polite, conversational tone:] I haven't asked her how she feels about spending more time together.
["Surely that's something she gets to decide for herself". If Yuuki weren't a near-stranger whose business she doesn't want to involve herself in, that remark would have been a lot more unsubtle.