Hi there,
Wow. This sounds like a tough issue and I never even imagined people could be so opposed to chickens as pets. Our neighbors all have barking dogs and they drive me crazy. There are no ordinances against that, are there?
I love the idea of pictures of your kids with chickens - showing they are pets and not livestock.
Anyway - when it comes to "sweet talking" people, I have had quite a bit of experience with this (not related to chickens). I've found that my previous expectations of those people can have an affect on the outcome. Maybe if you imagine the best possible outcome, imagine them accepting your home grown eggs as a gift, imagine them going along with your plan. Perhaps look for the good in these people - then when you go to visit them, you will have warmth and compassion in your heart and in your eyes as you speak to them.
I had a very grumpy neighbor. He was angry and cross with everyone, complained all the time. The truth is he was sad and lonely. I know this sounds ridiculously cliche, but its true. I was always super-kind to him, smiled at him, said good morning, and taught my children to be kind to him. He has done a complete turnaround with us. He is still grumpy, but he now smiles when he sees us, he waves, he even gave my kids $10 on their birthday.
You may think this is all nonsense or whatever, but I do believe our expectations can affect the outcome. If you expect it to go well, it very well might go your way.
I hope so!
Good luck, Peep-Show!