Today she let me pet her for a very long time. The next-door neighbor is completely cool with the fact that we're feeding her. Now I have to figure out how to take her to a low-cost vet and what the next step after that will be.
Yes, I'm smitten. :-)
She was rubbing up against everything on the porch, grooming there, starting to relax a little. She seems to want to make this her home, though she's still skittish around the kids.
I hope we can make this work.