People know what they are willing to do. Some people would take the dog, some people would not. But it is pointless to begin talking to them, and then take the dog. Since it's Tennessee and I don't know what these neighbors are like, I don't think its fair to give advice. If it was me, I'd offer to watch the dog during the day so it doesn't have to be outside (and they might just decide they don't want it anyway). Unless they are scary rednecks in which case I would just CONSTANTLY call animal control! I grew up in Atlanta and understand that some people are stuck in the mindset of "ME PERSON, HIM DOG. DOGS STAY OUTSIDE, DOGS ARE SECOND CLASS CITIZENS" (Half of my family still live in the south, that was not meant to be a mean generalization. My sister calls me all the time with stories like this about her neighbors

)
Some people don't understand YORKIES ARE NOT DOGS.....
They are little furry children

Good Luck!