How far is your coop from your neighbor's house? My coop is less than 50 feet from my bedroom and I never hear my rooster. Sure a shame to have to live next to something like that. Good luck! I hope the situation works itself out.
I learned a long time ago to do what makes ME happy. I agree with the poster above, if she doesn't like your rooster, she can move back to the city. You have the right to do as you please on your own property. If the law says you can have a rooster, I wouldn't worry about Fancy Pants next door :)