100% sure its cats? Lots of cats don't do much at night except hide due to foxes. Depends on the area though, our cats, and all other cats i know of around here all coem indoors at dusk -/+ a hour or two due to foxes prowling in packs. Get one of those sensor + water cannon style jobbies. You don't even need it on that often. Get one, hook up to hose pipe. Cats come close, get squirted with water and also surprised, not massively noisey but enough to upset cats or foxes, or anything. They tend to learn and start to avoid the garden.
Failing that, Valium in the dogs evening dinner?
As a non dog owner in a street with several dogs I can tell you your neighbors are more irritating than you are. My cats don't go out at night, but when foxes come in our garden my cats do watch them from the window, but somehow don't feel the need to tell everyone about it. Next doors dog, is actually quite loud and huge but doesn't react that often, its an irritating small dog several doors down that barks at everything and wakes me up very often.