Also, I think that Bella may be Josy's mom? Bella's husband in the wedding photo looked a lot like Josy's father; maybe they had some kind of falling out and he took the child. It could explain why Bella and Josy have such an instant chemistry. I can see this being a huge plot point in Season 2.
Sorry, but no.
The below is all pre C5 info so can be stated in the clear:
1. Josy knows who who her mother is and where she lives (ref. Dinner convo at her house during date).
2. Bella's husband left 3 years ago. If he took Josy with him, Josy would be approx 15 years old at the time. No way they don't know/recognise each other at the library.
3. Jill has been close to Bella for a lot longer than 3 years. She would defenitely know Josy if she were Bella's daughter when they met in the classroom.
From all angles, this theory can't be the case.