Hi, My neighborhood is zoned for 3 horses, no goats, yes to pigeons, no to roosters (that's why I hear so many crow in the morning), no pigs, etc. I moved here because this is what I wanted. My parents wanted perfect lawns, perfect homes, no cars parked on the road, no livestock, etc, and they moved into a deed restricted area.
If you are allowed to have a rooster, keep him. If your neighbor doesn't like it, she should have moved into a neighborhead that doesn't allow roosters.
I had a neighbor years back who moved out from the city to the country. The horse trails started next to my house. He always talked about how he loved the country life, but every time some horse (not mine) pooped on the road between our houses, he would come to my door and complain,even ask my DD to clean it up!!!!! I guess he felt that I had horses, so I was responsible for the poop on the road. That was only one of the problems. Karen