For a status-conscious Chinese public, this won’t go down well.
From NYTimes…

For a presidential meeting that is intended not so much for substantive agreements as for relationship-building between Mr. Obama and Mr. Xi, Mrs. Obama’s absence will rule out some extra dollops of personal diplomacy. And according to China experts in both countries, it is certain to be noticed by a Chinese public eager for the sight of their first lady joining America’s own groundbreaking presidential spouse on the global stage.