In reply to Sharp:
I'm tempted to sympathise with your neighbour rather than you.
In short, your partner has a cat. Their cat annoys your neighbour, hence, if there was any transgression, your partner was first. Your neighbour is actually entitled to enjoy their garden as they wish, not how you wish.
The neighbour has - perfectly reasonably - installed a device to get rid of cat, to which you have objected. So, first you cause the problem, then you object to their attempts to mitigate the problem you have caused. Then first your partner, then you, go round and bang on their door at 10pm to object to their mitigation to the problem you caused. Then you call the police on them.
Well done for dealing with the issue in an adult and responsible manner and not escalating it at all.
For what it's worth, I love cats. However we have an alley down the side of our house which, until we got a cat scarer, reeked of catsh*t from neighbours cats. It really was not pleasant and meant that if we had friends round with kids we ended up clearing a lot of catsh*t out which we were in no way responsible for. It was extremely annoying. However you say the issue isn't poo.
The way you are writing comes across - as others have already pointed out - as someone with a massive entitlement problem who thinks that they can inconvenience and upset anyone else as much as they like but as soon as anyone else objects then it's nuke them from orbit time and get them into trouble with the police, which may have massive repercussions including losing the person their job and their home.
Presumably you don't mind this.
Obviously if the reality is totally different from the above then fair enough, and it may just be the way you are coming across, but, in my view, you are not coming across well in your telling of the story.