http://library.municode.com/index.aspx?clientId=10092
The above links to your parish ordinances. Section 4 on the left side of the page addresses animals, and section 4-37 addresses nuisance animals. It is in Section III once you click animals in the left hand column. In Section I it stresses owner responsibility for animals behavior and their welfare.
4-37 says that dogs and animals are not allowed to roam free and cause a nuisance to neighbors in your parish. There are penalties for violations: $500 fine, up to 30 days in jail, and community service.
I cant copy and paste them, but maybe you can print it and take it to your neighbor. The fine alone would make me not allow my dogs to roam, if it were me. Ask her to pay you for the chickens and one week of food you wasted on them, and tell her she is lucky you havent called the police.
I assumed you are in LA, so if not, this does not apply!