How to use javascript to select (a) child(ren) element(s) of a hovered element?

assuming I have a (very large) div tag and inside the div tag I have a (normal size) button, now I want to be able to create a shortcut that if a user is hovering over the div tag, they can press return key to click the button.

$(window).keypress(function(e){
  if (e.keyCode == xxx) {
    $('div').hover(function(){
      $('this button').click();
    });
  }
});

This is how I imagine it might look like in jQuery (didn't work obviously). I am open to suggestions. jQuery solutions are fine, plain javascript solutions are even better.