Can you hang some tarps or something over your fence so neither dog can see through?
Honestly based off of what you said I'd give up on the idea of your neighbor doing anything to help you, so you need to look at this situation from a "What can I do?" lens. Maybe putting up some tarps will solve the problem or at least make it tolerable for you and your dog. You could try a bark deterrent such as this and use it with the other dog when he's antagonizing yours through the fence, although it's not guaranteed it would have any impact.
Glad to hear that you're moving, at least you're not faced with having to deal with this for eternity.
I carry this. I have never had an occasion to use it, which is good of course, but that means I cannot tell you how effective it is. I suppose it will vary from animal to animal anyway. Other similar products come up on Amazon on course. Bear spray comes to mind but that may get your pup in the spray. If they are feral cats then I doubt water would do any good.
What city do you live in? Here in Atlanta we have organizations like KirkCats dedicated to trap-and-spay of cats. I know you said traps aren't a viable option but maybe they will have other ideas. At least they might be more helpful than the city government.
As stated by others e collar on aggression is not the answer. Sometimes it can actually increase the aggression. I would recommend this spray. Pair it with a "safety word" works really well to snap them out of it, eventually you'll just have to use the word.
Barking is a use for it. This is what we use.
I went through the same thing with mine at about 9 months where he would get super aggressive of a dog that was within a few feet of my personal bubble. I worked on it with giving him a lot of treats when other dogs came over to say hi, and kept a "pet corrector" around for times at the dog park. He completely cut out that behavior until just recently (4 months later now) where he did it with a friend's dog while on a camping trip. I thought it was due to his exhaustion, but it could be a combination of adolescence, mood swings, hunger, tiredness... All I can say is try to meet with your friend again and show her that everyone's a friend, give treats when she does well, and I definitely recommend the Pet Corrector
My Akita mix mutt LOVES to stand up and greet us when we come home or have food. He luckily doesn't put much weight into it- mostly just stands in front of us on his back legs like a little meerkat. Adorable, but we figured we would train him for the sake of manners
We had a trainer tell us to turn our body away while saying "off." Don't put your knee up or touch the dog in any way, just turn away and say off. The other commenters are right about ignoring the dog until she sits.
If all else fails, I use Pet Corrector (basically a can of compressed air that lets out a hissing sound as a warning). I don't like to use this much because I'd rather use positive reinforcement, but it's really effective for getting a dog to stop whatever they're doing- often I just show him the little can and he knows to behave.
Good luck! She has such a sweet face
One of the reasons to not get small dogs. They yap-yap-yap like crazy.
Have you tried things like the pet corrector: http://www.amazon.com/Company-Animals-Pet-Corrector-50ml/dp/B0124G4DV4/ref=sr_1_2?ie=UTF8&qid=1458144648&sr=8-2&keywords=pet+corrector
or a spray bottle?
I don't blame you for picking him up. My trainer recommends compressed air like the pet corrector to stop dogs from getting near yours. I wouldn't use it for training but it would scare a dog coming towards you. https://smile.amazon.com/Pet-Corrector-Behavior-Training-Harmless/dp/B0124G4DV4/ref=sr_1_3?keywords=pet+corrector&qid=1560182346&s=gateway&sr=8-3
I would carry a pet spray for the protection of your dog and the other dogs. There are two great option. Both make a sharp hissing noise, one also has citronella. Neither hurts the dog, but should scare away the dog from following you. Biggest problem is it may scare your dog also.
Side note, I would never use the spray as directed on the package. Emergency use only. Better to scare 2 dogs than to have your dog hurt another and then have a bite record or worse.