BTW, Nancy has just landed in the Republic of China
Not that it really matters, but I wonder which would actually bothers the PRC more. I would have thought that the real source of irritation with, "Republic of China," is that it references the name used by mainland China up until the revolution of 1949, thus manifesting Taiwan's historical claim to be the legitimate Chinese government in exile.
To sum it up, most important for CCP is that Taiwan is considered Chinese. I know CCP likes to play the long game, but at some point Taiwanese cultural identity will have shifted too far for this to work. I think it is close that that point, and that in another generation it will most likely be there.