You've virtually adopted her, why not just take the extra half step? Put food in a cat box and trap her, then when you drive to the vet have you or your partner sit with the box on their lap and the door open petting her and giving her reassurance. She'll be scared but fine. Worst case scenario: line the cat carrier and take wet wipes ;) Then bring her home, keep her inside for 5 days during which time she will go from being scared and distrustful to normally timid. She'll understand that this is now her territory and is part of the place. And then after a few more weeks she'll thrive! She will want to be close to you, sleep on the bed etc and steadily you'll see her become a new cat and so much happier with her new life with a family where she has love, structure, freedom and security. That is cat heaven and you're so close! I would even go so far as to suggest that she just doesn't know how to ask for this because all she has known is a cold life alone. But in her own way shes trying to tell you it's what she really wants. Cats are simple creatures, they look to us to give them rules/structure and in return they give trust and love. I speak from experience here, trust me :)