And look at the hat on Emily's childhood bed (in the '60s or '70s):
Don't look at her boot lamp, though. We're calling dibs.
It's the same freaking hat -- passed to Andy from his mother, who apparently misplaced the white lace in the middle at some point, possibly after running out of TP in the bathroom one time (you can still see the faint imprint where it used to go, though). While we're at it, look at Andy's mom and Emily side-by-side:
If they're not the same person, Pixar's getting pretty lazy at character design.
True, Jessie and Andy's mom don't recognize each other, but it's been a long time. There's no reason Andy's mom would realize Jessie was her exact same childhood toy, and there's no guarantee Jessie would recognize Emily as an adult. She's used to living life as an immortal, unchanging plastic being, so the idea that her old friend could morph into an even bigger giant with increasingly decaying flesh on her face must seem pretty bizarre. Finally, as you may have guessed from the fact that we keep calling her "Andy's mom," the character's name is never mentioned in the movies, so it could easily be Emily.
Sure, the creators themselves have seemingly shot this theory down, but this is Pixar we're talking about -- they could simply be lying to try to maximize the amount of emotional damage they'll do to us with the next movie.