Just my 2 cents:
Have you gotten the police involved other than filing a report and have they questioned the neighbor you were having problems with ( the fence/gate incidence)?. I think that is where you should be concentrating your efforts. I doubt she will be in a shelter if she was stolen. Since the guy that damaged your gate had to pay you money he probably took the dog as a way to get his money back - either to keep or resell. I would keep a real close eye on your neighbors friends and start following them home. They may be driving a different car.
Have you gotten the police involved other than filing a report and have they questioned the neighbor you were having problems with ( the fence/gate incidence)?. I think that is where you should be concentrating your efforts. I doubt she will be in a shelter if she was stolen. Since the guy that damaged your gate had to pay you money he probably took the dog as a way to get his money back - either to keep or resell. I would keep a real close eye on your neighbors friends and start following them home. They may be driving a different car.