I am also a parent. My thoughts are a little different... assuming chickens are legal in the OP's locale. I think the OP's mom would be right to stand her ground on the chicken complaint. Whiney neighbors are no reason to deny a teenager the joys of poultry keeping. Chickens are so much healthier than, say, terrorizing the neighborhood or getting into drugs or something. This teen seems to be on the right track, why take that away from your kid just because a new neighbor doesn't like your lifestyle? Why is this mom letting a new neighbor dictate her family's way of life? Just my opinion, but I would not tolerate it... period.
I understand where are you coming from, honestly I feel very similar. Here is the thing...California. Zero offense towards any Californians, but following is not "the exception" There is a reason some counties vote to secede every couple of years.