I would supervise the dogs when they go out, make sure your nieghbor isn't doing anything. Even if it doesn't seem like it, all of the commotion and/or your nieghbor possibly yelling at her or worse could scare Benji. Border Collies are the most sensitive dogs in the world! A small disturbance can freak them out, because they are very observant and smart. Have you tried taking her out on walks to get her to go potty? do everything to build her confidence, go outside with her, play ball or whatever games she likes out there, give her lots of treats and make it a very positive experience. Also, try to introduce her to all of your neighbors (except for the one who doesn't like her, of course, unless its possible), have them give her treats and let her know that the people around you are nice. You might also want to enlist her in obedience classes, it will help her gain confidence and you said she isn't listening well, so it should probably help that. You could also call a behaviorist to just talk or even come over and check everything out.

Don't force her outside, coax her out and be very patient. Border Collies sense everything, even if you're slightly annoyed or mad at her. If she is really a complete nervous wreck, you could consider finding her another home, but who knows if that would even solve it? Maybe all of what's gone on has really freaked her out, and she would act the same in some one elses home?... and would they then want to take her to obedience and help her to get over this? I would definitely recommend you try Obedience, desensitizing, and just encouraging her lots.

good luck!!