I'm glad you're ok for food. The way I look at it is, the dog's got you as probably its one (and only) defender/advocate, and it's a responsibility all its own. If you absolutely have to turn it over to a shelter, I'd research no-kill ones. I'm sure there are pit bull rescues, too, to deal with all of the dogs who come away from dogfight situations. Someone from a rescue might be willing to make a drive to pick the dog up, and at least then you'd know the dog would be fostered until a home was found. I'd stay as far away from kill shelters as you can.
Re: the cat...not doing it to impress anyone, I just had a major fucking problem with this:
...and fortunately, so did the animal control people, so they assured me the law was on my side with this one. I felt guilty, but I just couldn't stand to see her like that anymore.
She's very happy and healthy now...has regular vet care, all her vaccinations, successful spay and hernia repair, and regular flea/heartworm treatments: