For the hen on the eggs, you may be able to slip in when she's off her nest to candle them and determine if they're developing. You can, of course, destroy the nest and break the broody chicken yourself either way, but if seeing how far along they are may influence you, you can candle them. What I would do is use a BRIGHT flashlight (cellphone lights on android smartphones work well for this), bring out a heavy, dark blanket when the hen gets off the nest and check the eggs.
For the legal standpoint of things, do your research into it!
What is the specific code or ordinance you are in violation of?
Are your neighbors with animals also in violation?
When did this go into place?
Does your state have any grandfathering requirements regarding these laws?
Document the animals on neighbors properties.
How are the laws changed?
Can you contact neighbors and devise a campaign to change the law?
A broody hen on eggs makes a GREAT social movement mascot, especially if there are children involved.
But neighbors who are also accidentally in violation or could be "next" on the chopping block make an even better one.
If it's an HOA, who is on the board? Can you motion to dissolve it?
Do state laws protect your right to keep your animals?
Can you afford a lawyer, even if it's just for a couple of legal notice letters to cause a postponing of removal?
Start there, build your case, present it to the city council. Call news stations and get them involved. Make a big stink. Research other places that have started allowing 'city chickens', propose new ordinances, and document how much it cost those cities to try to block those proposals. Some cities have wasted tens of thousands of taxpayer dollars trying to block city chickens. Point out how much that would damage the community, where that money could go towards improving infrastructure.
There's a lot of good info under the local laws and ordinances section of the forum. I would split this into two topics - one on legalities, one on the chickens.