Sell the house, get another one where the neighborhood isn’t poisoned by an HOA and the officious Stasi-informant types working for it.
As far as constructive advice — is the playhouse a permanent structure, or just a freestanding object like a barbecue? If it’s the latter, is there any rule against placing a (slightly) movable object in your own back yard within reason?
As far as the neighbor, I could suggest a thousand means of making his life unpleasant, but I can tell you’re a reasonably intelligent person from your writing. I’m sure you can think of something good.
On second thought, the guy is a dickless, spineless little jellyfish and will be the source of his own failure in life. If you have problems with something your neighbor does, you man the hell up and ask them politely to change it. You don’t submit a report in triplicate to the “proper authorities.”
