Forget the unified Pixar theory. Or rather, let's get more granular than the unified Pixar theory. Have you ever given much thought as to who Andy's mum is in the movie Toy Story?
Random, I know -- but, hear me out!
According to Jon Negroni, the movies have given us subtle clues as to what her identity is -- and who she might actually be is surprising. First, we have to look at the initial picture in this post. See Andy's hat? Now compare Andy's hat to Jessie's hat:
There are more similarities between Jessie's hat and Andy's hat than there are between Andy's hat and Woody's, no?
Now let's look at when Jesse is introduced to us -- this is the hat we see on Emily's bed (Emily, if you don't recall, is Jessie's original owner).
Same hat! (EDIT: there is the issue of the lace band, though if we assume the hat is old, it's not a stretch to think the band either faded, or was lost -- they still have more overt similarities than Andy and Woody's hat do). We also know that Emily would be old enough to be Andy's mum by the time Toy Story 1 happens, and that when Jessie was given away by Emily, the hat wasn't necessarily one of the items included with Jessie. Emily might've kept it..and then maybe given it to her son, Andy. And Negroni also notes that both Emily and Andy's mum have similar hair colour of strawberry blonde. You can catch a glimpse of that here, along with the fact that Emily didn't give away her hat:
Obviously, none of this proves they're the same person -- but hey, there are enough similar details to consider it for a moment, no? And if Emily and Andy's mum are the same person, it would make the story better, I think. Both characters had a strong connection to their toys growing up, both eventually forgot about their toys, but both passed on some part of that love to other kids. Sad, but lovely in a way.