First ... I am so sorry you find yourself in the messed up predicament. People can be jerks!
Take a deep breath and call your zoning office. Today. NOW, if you can. Explain the situation with the shared lots and your neighbors and find out how to file for a zoning variance. Do NOT play the failed relationship or selling eggs, or even the "nasty neighbor" cards. For now, at least, this is strictly a zoning issue. Your zoning office (I believe it's in Bel Air) will know if there are exceptions and can advise you on how to file the variance. DO IT THIS WEEK! It's easy to do, it just takes a little time. You'll need to get your neighbors onboard, as they'll need to verify that the birds and the property are shared.
Move quickly on this, as you'll have to attend a zoning meeting, and you don't know when that is scheduled. If you miss it, you have to start over for next month's meeting.
If one of your neighbors has children under 18, have them contact the Agricultural Extension Office and get them signed up for 4H. It's an awesome, inexpensive (how does $10 a year sound?) program for youth and they get to show at the County Fair. They can also qualify for a zoning waiver for a 4H project!
Don't write off your birds, yet. You can do this!