I'm so sorry you're having such trouble with a nutso neighbor. I wonder if the code people can send the cops to their door for wasting city employee time? That's hilarious that the code people had no idea about Pekins!
We bought that chicken tractor from you a few months back, and my hubby said your place was so clean and neat you'd never know you HAD chickens!
(Our four silkies and 3 three-month old chickies are loving the tractor!)
I hope you can get to the bottom of it and get it worked out. I wonder if you could just take some eggs around to all the near neighbors, including the complainer, or maybe some nice home-baked goods, and be really friendly, and maybe that would get them to stop. I'm torn between recommending being nice and being nasty. Being nice might be more effective at stopping things. A cranky visit with them will just make them feel more justified in their harassment, I think, because it will reinforce their unjustified low opinion of you.
Keep a copy of that email on cheapcycle. You could end up using it in court if this neighbor goes too far with something. Also, it could be used to show defamation of character. They're lying about you on a public forum. Probably not completely illegal since they're not naming you or saying exactly where you live, but you never know. I'd actually send copies of her emails on cheapcycle to the code enforcement and health departments. Maybe they can take some action since she's publicly defaming you.
I am sooo glad we live way out in the boonies!