I mean, if you know more than the QM about how the proposed plan would go wrong:
By all means share with the group. I'm keeping an open mind, what are we all missing?
From what I recall:
The IRG is loyal (mostly), loyal to the Empire and the Empress. This loyalty has a hitch because Princess Yui is outright better at being Empress than Meigyoku herself. Which means Princess Yui puts the institution under stress merely by existing and further by acting as second in command of the Empire. I think it was brought up that if Yui tried to ascend the IRG would have a bloody civil war?
Which is why Major Yui is keeping an eye on Princess Yui.
Asking the IRG to take up tasks is already an awkward thing to do because the more problems Yui presents the more compelling her possible takeover becomes. Perhaps she could present things by claiming that her personal resources are currently insufficient? And bring the Commanding General face to face with Meigyoku to prove Yui's own superiority in all ways?
-[X]Personal loyalty to the Empress: Her Imperial Majesty has privately requested that this investigation be made, as the matter of military weapons getting into the wrong hands is a significant priority to her. However, it has become much larger than was anticipated, and she needs loyal, capable people at this earliest, most tenuous date of her role.
--[X]Bait the hook: If the General wishes, a personal, private meeting can be arranged to address her concerns about our "influence".
Yeah...
In all likelihood the write-in is not going to cause huge issues, since Yui has cheated with S-Rank politics before. A paranoid reading of the vote might get a reaction about what we didn't say, but could be assigned to her words.
"I, Princess Yui, should be accepted as having imperial authority when I make requests of the IRG."
"Any competent subject of the Empire would accept that the Empress would and should agree with me about everything." (the current Empress should not rule at the present time)
Which is something we don't want to communicate.
I don't want Yui to invoke loyalty to the Empress here. Hiding behind Ahri's tails could provoke a bigger, nearer problem. I also don't want to carelessly assert control over her Imperial Majesty's schedules. Princess Yui has control, but should be using it to solve Ahri's problems, not her own
I'd prefer to offer a personal favor myself. General Manandal, from what little Yui knows, must have effectively traded favors to succeed in the past. So she's likely to put some value on Yui's offer. Since we're both on the same side that favor being called in shouldn't be something we're opposed to doing, and the time or effort is a fair trade because getting assistance saves us time and effort now.