I think it would be much better if the OP told the neighbor that she (the neighbor) should put some poultry netting a few feet on her side of the fence to keep the dog from getting close enough to the fence to see the chickens. I am so glad that none of my neighbors' houses are that close. If that dog is such a nuisance, the owner should hang tarps around her entire property so it can't see out and yap at everything. I still say it would be best to ignore her for now. Jumping through hoops for those type of people just makes them feel that they can control you and push you around. First she will want the extra poultry netting fence. Then she will want you to get rid of the chickens because the dog doesn't like the crowing or the egg song. Then you won't be able to have any pets because it upsets Fluffy so much and makes him bark. Then the wind will blow leaves from your tree into her yard so you'll have to cut it down. Then she will find your lawn ornaments unattractive so they will have to go. Oh and that compost pile is very unattractive - can't you get rid of it? Oh, and can you leave the garage door closed. It's very unattractive when it's left open so long. Please take down the bird feeder. It's attracting squirrels, and all those song birds and squirrels are upsetting Fluffy again.
Sorry to go on like that. I just can't stand neighbors that are nosey or try to control aspects of other people's lives that are none of their business. There are some people that believe that their yard is theirs and everybody else's yard is somehow community property. They make demands and expect the world to accommodate them. If you ignore them, they usually fade away.