A word of warning...I have the exact same situation. CC&Rs say no poultry or fowl. No HOA in over 20 years so we are governed by county zoning, which allows chickens, even a rooster. BUT ONE neighbor objected (just one) and threatened to take us to court. THAT'S how CC&Rs are enforced in the absence of an HOA. Our lawyer told us we would lose in court, have to pay their court costs AND it could easily cost $10k or more. We got rid of our chickens. All our other neighbors are fine with it and this neighbor is around THE BLOCK. Over an acre away. Never has spoken a word to us in 8 years and our coop and run are lovely, like yours. We had our chickens for 3 years before we got the letter from the attorney saying they were going to sue, but they actually tried to file a complaint with the county just a couple of months after we got them. The county told them we were in compliance, but did not tell us that if they sued then the CC&Rs would trump county zoning. The CC&Rs go with the land forever and all we can do is get them amended or revoked. But they JUST renewed for 10 years last year and we can't do that until 2025. Another legal screw against us.
All we can hope is that they are moving. I also am thinking of getting a petition together of all the neighbors who don't mind chickens and see if that will change their minds (I don't think so). Their only reason for wanting them gone is that they say it hurts their property values. We're all on 2 acres and in a horse neighborhood. Some people just suck.