Well, whilst she's still somewhat tied to Patrick if you don't get them, he factually has no power over her. They might not find that out if you don't get them, but he's given up trying to control her and threaten her college education as seen at the end of Ep 11 when Maya and Derek go see him. So although it was all a bit of a lame duck in the end, it might not be much of a factor since she doesn't have anything to worry about anymore.
Also, when you think about it, she kind of chose Josy over Patrick in that moment, finally. This whole ultimatum incident was kind of about that; her Dad making her choose between obeying him and dumping Josy, or staying with Josy and risking her college future. She was torn between these 2 things and that certainly could have been a factor in this rift between the girls because Josy would have wanted Maya to just choose her outright but instead she couldn't choose and so it probably made Josy feel less important. But in Ep 11 if you didn't get the papers, she's essentially finally decided that she doesn't care what her Dad may do to her now because she's tired of fighting him and so she choose Josy here, chose not to let her Dad get in their way with his threat. But Josy didn't like it because she still doesn't like the idea of Maya being beholden to him and having some control over her, but Maya's essentially just said, "fuck it", and is choosing not to care what he might do to her anymore, so it's her finally taking a stand against him. It just didn't feel good in that moment for Josy, but once she realises Patrick has relented then maybe they can move past it.
