I believe this is Norman Spinrad's "Year of the Mouse", originally published in 1998 and collected (among other places) in "The Year's Best SF 4" in 1999.
The first line is what you thought was the title:
"Mess not with the Mouse."
Disney wants to release a movie called "The Long March" in China, but the Chinese government gets offended and threatens Disney, only to have it not go as they'd like when Disney doesn't back down:
"How can they expect to get away with this affront to the Middle
Kingdom?" he demanded. "How can the American government permit this? You did make it clear that we may retaliate against other American
corporations as well?"
Xian Bai nodded miserably.
"And?" demanded the Deputy Minister.
Xian Bai took a deep breath, fixed his gaze upon the desktop.
"They... they issued their own ultimatum."
"An ultimatum?" whispered the Deputy Minister, clearly dumbfounded.
"The People's Republic of China must allow THE LONG MARCH to open
simultaneously in no less than one thousand theaters nationwide with Disney to retain sixty per cent of the gross, must cede the necessary real estate for the establishment of no less than one thousand Panda Pagodas, plus Disneyworlds in Shanghai, Peking, and Hong Kong, and grant a one hundred percent tax abatement for a period of fifty years on these properties, or...
Disney releases balloon antennas:
"Do you realize what this is, you imbecile?" he demanded.
Xian Bai regarded the grinning balloon face in perplexity. All seemed quite ordinary, except for the bulb at the end of the long white rodent's muzzle, which, instead of the traditional black ball, seemed to be a small silvery packet of some sort of electronic circuitry....
"This," said the Deputy Minister, poking Xian Bai's nose with that of Mickey, "is a satellite television antenna!"
