Her barking and aggressiveness towards your neighbors dogs, and none towards your trainers dogs, might be because of perceived boundaries. Your neighbors dogs are in her boundary, therefore she is guarding you and her boundaries. I hope the class goes really well for both of you, Gina has benefited very much from all the classes we have taken, so have I. Good luck.
Cheers Quad & Gina
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Assume Nothing, Question Everything, Start Thinking!
RIP Megan 3/1998-5/28/2013