I have three (spayed, female, mainly indoors) cats, and they use a rather snazzy covered cat bog (£16.99 from a well known catalogue shop) We do not have a cat flap, and the little darlings are always in at night.
Two neighbours own the biggest bastard (un-neutered) almost feral tomcats ever who are out all hours and piss and shit not just in our garden, but break into our house through the teeniest gaps in windows and spray everywhere. If they can't get in they piss on our rotary drier. Or trash our veg plot. Two out of our three cats will not go out without one of us to guard them. Those tomcats are terrorising the whole street.
One of the owners thinks her cunty cat is amusing, the other owners are not the approachable type.
If my conscience would allow it, I would deal with those cats, permanently. Luckily for the tomcats, my conscience kicks in for things as trivial as being given tuppence too much in change, so certainly wouldn't stretch to more nefarious acts...
It's bloody distressing being at the mercy of other people's animals - the smell, the mess, the damage, being too embarassed to have guests round etc. The costs of buying useless deterrents. The affect that it's having on my girlycats.
If I were braver, I'd be flinging shit and piss over the fence, I can tell you. At the end of my tether with the whole thing :(
So, both you and your neighbour were being unreasonable. That said, you are both very lucky that you are both of the ilk that will sit down and resolve challenges together.
We have no such luck.