I hope you'll still post pics of your set up, but from all you have described it sounds like your set up is secure. A coyote would probably kill the same way being kin to the dog but if you see no point of entry then how did one get in i think I'd install keyed locks on your run That would...
A dog would grab a duck in the middle of it's back and shake. Would your neighbors do something so awful as to open your pen and let their dog go after your ducks? I cannot image but people do awful things. So very sorry for your losses, and when you say looks like someone stuck their hand in...