I’m not sure how kittens can ruin a gate? Or a car?
Also, how on earth can you have a vicious dog in your garden which, as you say, would kill cats
, when you have your own cats and a rabbit?
Can I ask why your cats can’t go out? If you’re worried about roads etc, did you know you can get a wire around your garden which emits a beep and gives cats a minute static shock if they go past the beep (they wear a special collar when out). At least they can get some sun and fresh air and chew the grass etc which they need for digestion.
A normal trellis on top of a fence or gate probably won’t stop nextdoor’s cats, but you could try fitting a trellis that’s unstable because cats won’t climb over anything unstable.
Or you could ask your neighbours to fit a roller to the top of their wall? It’s like a long rod that rotates is the cats paws can’t get purchase on it. But this won’t work if they can jump over anyway due to trees etc, Also, if they’ve scented out your garden now as territory they will probably go around and find a different way to get in.
Have a google for “cat containment”. There are plastic prickly surfaces you can lay in top of walls (these don’t work), rollers (never tried) or wobbly trellis things that will deter cats.
There are sonic detectors that emit a high pitched beep but these don’t work. We have 4 cats. They all say next to the beeping sensor and howled at it to shut up.
The best thing to keep them out would be to let your own cats out! Especially if nextdoor’s are only kittens.