Thanks to everyone for all the great comments and suggestions.
In the last two days I've been turned down by two more sanctuaries. So our adventure continues.
If we could legitimately get her rabies shots, get her spayed and be able, if needed, to get her medical attention, we'd gladly keep her. But she is just considered wildlife. Just a nuisance. And further, it's illegal for vets to work on her.
It was recently suggested that she might be able to live on the private duck club land not to far away, but it turns out the coyotes get more ducks than the hunters, so that's out. I love that story. The wily coyotes are more capable than the hunters!
It's so interesting that this fascinating, friendly, fun loving and very adaptable little dog can also be a serious menace in another setting. I'm still struggling to see the difference between wild and tame. She is different than other dogs I've had, but her environment here has eliminated the struggle for food and the fear of humans. Maybe the biggest difference is her determination to do the things she wants to do. She has a simple routine each day and hunting, competition for food or hunger are not part of it. She dose patrol around, plays keep-away, marks her territory, hides her food, sleeps during the heat of the day and has very predictable hours. She also loves to spend time with us in various settings. But she doesn't seem to have much interest in pleasing us. Other, more domesticated dogs, are more responsive to commands and more interested in their master's mood or direction. Bei Bei, for instance, is always ready to go do something and is just waiting for me to say so. Her tail is always wagging. She loves to meet new people. I can take food away from her without incident and I can tell her to "look" when there is something interesting, and she will. She also is likely to wander off. Sandy, so far doesn't wander off at all and always sets her range based on where I am. But recently BeiBei wandered off and took Sandy with her. Sandy was troubled by it and only went a short distance. When we were looking for Bei Bei, Sandy was trying to show us where she was by looking in that direction and being uneasy. Things were out of order and she didn't like it. Order and routine are important to any dog, it seems, and maybe even more to this one.
On the other hand, domestic dogs can be very vicious. They can become wary and mean, pack up and attack other animals, etc. Our dogs miss us when we are gone and we always get a nice greeting. That's one of the fun things about dogs that we all love. Sandy seems to want to go when we are getting in the car and she can ride for hours without a problem. But if she has to be left behind she just watches us leave or trots off to do something else. If she is up during the day when I get home, she comes over for a nice greeting or to check my hand for a cookie. If we drove off and left Bei Bei out, no telling where she would be when we got back. Eddie is even worse with his separation anxiety.
It seems there is something to "wild" vs "domesticated", but a lot of the difference is environment. I can never really put my finger on an absolute difference with Sandy. At least that's what I see with this particular dog. I will also admit I don't trust her completely. For instance, I'm careful with Sandy around my young granddaughters. We've had no problems, but she is an unruly pup in some ways and everyone who meets her is expecting "wild" behavior. The same behavior that amuses an adult can scare a child. It's more that she lives in her own world. Many have described her as being a lot like a cat.