Seconding Midgen's suggestion. Email her boss explaining that your boss needs for Y to be done, and that he feels X is the best person to do it/only person who can do it. Then just ask him politely if he would be willing to make <whatever of her time is necessary> available to do Y.
And that's all. I wouldn't go into any history or "second level" explanation; just the direct causal "why". Boss wants A, therefore B. I think the less you say, the better. You haven't said anything that looks like you're blaming your boss, or that you're blaming X, but X is free to believe the former and your boss is free to believe the latter, if they want to. Meanwhile, it's just a vanilla, proper-channel, cross-department resource request as far as X's boss is concerned.
Midgen wrote:
Nah, keep it all above board. Make sure everyone knows what's going on...
It's a passive-aggressive response to his passive-aggressive BS, so proceed at your own peril..
This is almost always the best policy. Having a bunch of BCCs flying around is a good way to create more drama.
That said, since you've already talked to X about this twice before, even a no-frills email like this could be interpreted as going behind her back, and leave her wondering what conversations might have been had about her that she
wasn't CC'd on. I would be inclined to give her a head's up and a (private) word of explanation about the situation before you send the email just to make it clear that you aren't in any way complaining about her to either boss. Perhaps just something simple along the lines of "I'm sorry, X, but my boss is
really insisting that you're the only person who can do Y. Apparently he wants this more urgently than I initially thought, and I realize it just wouldn't be
fair to you to ask you to totally rearrange your schedule for another department without clearing it with your boss first".
If she's someone you can trust, you might even just level with her about the whole situation (i.e. "I'm caught between my boss and looking like a huge jerk. I hope you understand.")