My neighbour is submitting false complaints to the council about my family that could end in thousands of dollars in fines. What can we do to stop her?

My family has been living in this house for the last 7 or so years, and we've had the nastiest old cow as a neighbour for the entire time. On the very first day we moved in, she came over to tell us she worked for the city council, and that her bedroom window overlooks our pool, so under no conditions can anyone have sex in it (yes, our pool, on our property). If that wasn't creepy enough, she tells us she can hear every word that is spoken in our back yard, and she would appreciate it if we didn't speak too loudly while outside.

Fast forward a few months, and we're playing dog-sitter for a friend. This dog is seriously the nicest, most quiet dog I've ever seen. Not to mention, she's getting old so she isn't very active. We only look after this dog for about 6 days, and we get a noise complaint and a threat for a $200 fine from the council because of this dog barking. We called the council and tried to find out WTF was up. Suddenly, the matter is dropped, and we're told to not to worry about it.

A few years pass, and every couple of weeks she comes over screaming at us about our "family noises" interrupting her sleep. For the record, my family consists of 4 adults, one of which is severely disabled, so it's not like we're having wild parties or anything. She told us she tried to report us again for noise complaints, but her co-workers in the complaints department talked her out of it. So, as a final resort she comes over to scream at us.

A few months later, our house gets broken into by a group of teenagers. There's cops all over our street, court dates, charges pressed, serious business. The people who broke in even came back and vandalized the house as revenge. The police advise us to get a dog, so we do. We get a dog, but not a big vicious one. Just a small-ish mutt, because what we want is an ALARM dog, not an attack dog. Guess who comes back? The stupid bitch next door waits until 3am to come over and try and beat our door down about this dog. A few days later, another noise complaint with another $200 fine threat. Same thing as last time, we confront the council and it's dropped.

A few weeks later, another warning. This time, it's about our so-called hazardous, untidy, disease breeding garden. Sorry bitch, but anyone who's stepped foot in our yard knows that our garden is run like fucking Nazi Germany with my mother as Hitler. People have come over to ask us what we do to our yard to keep it so damn perfect all year round. So, this new complaint is obviously fabricated, but since we're told that we'll be fined $300 initially, then $500 for every day afterwards that it isn't clean, we couldn't just ignore it. We ring the council, and invite this guy over personally to walk around our garden. He accepts our offer, but doesn't show up. After two weeks, we call him again, and he's like "oh, I sent someone over to check it out and everything is fine". He didn't. No one came around, and all of the council workers we spoke to were mysteriously avoidant of us. We gave up and continued on with life.

Weeks later, a new noise fine. Same deal, they drop it after a phone call. We decide to set up a barricaded, locked area that the dog goes into every night at 6pm, on the opposite side of the house that this bitch lives on. Everything seems to be working out fine.

Today, there's a new fine, for another noise complaint. I'm so unbelievably tired of this that I'll ring the council, sort it out, then sort her out personally. The question is, how?

I'm leaning towards purchasing a slingshot and taking out a few windows, but that's obviously illegal. My plan B is to report HER, and hopefully get her sacked for misuse of power or something.

Any better suggestions?

TL;DR: Our neighbour is psycho, and she works in the complaints department of the local council. The crazy bitch has repeatedly filed false reports against us. We've kept all letters and voicemail from the council.