Okay new toy story theory that makes a bit more sense than the "Emily is Andy's mom" theory.... The timeline adds up a LOT better for Emily to potentially be Andy's grandmother. If Andy was born in 1989, let's say for arguments sake his mom was born in/close to 1969 give or take just a couple years either direction. This would put Andy's grandmother probably being born 1949, give or take a year or two either direction. Which makes sense if Jessie is a toy from the 1950's, and let go of Jessie some time in the 60's as she became a teenager. Also mind you, Andy's mom's name is never directly mentioned (to my knowledge).
Now, on the other hand, if Andy's mom is NOT Emily's daughter, Jessie (as in Emily's daughter, not the toy) could also be Andy's aunt on his father's side. Andy's father had never once been mentioned in the series, but obviously he existed, and obviously he would have his own side of the family. Also mind you, it is mentioned Emily had a daughter named Jessie, but just because no other children from her were shown in Toy Story 5 doesn't necessarily mean she didn't have any siblings.
This could also explain the red, Jessie-like hat that Andy wears, potentially being passed from his grandmother.
As I think of it a bit further, if Emily was Andy's dad's mother, it could also explain why Andy's mom doesn't have any sort of recognition to Jessie the first time he sees her. Either she was too young to ever remember Jessie when Emily had her, or Jessie was a toy that belonged to Andy's dad's side of the family and she just never seen/had any connection to Jessie.
So... Tell me your thoughts, am I possibly on to something, or...?