Emmsy sounds like someone's gooey nn for their grandmother Emily. Like Mimsy or Momsy or something.
Millie doesn't really make all that much sense as a nn for Emily. And it sounds like a flaky, flighty old lady who's always getting scammed and falling off stepladders and atacked by chipmunks.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin