If it'd been me this bitch had called the police to badger over a damned bb gun, you'd better believe I'd be siccing as many city agencies as I could on her. For starters, I'd call the local animal control and tell them she's mistreating her dog. Also call health and hygiene and complain about uncleaned-up dog crap in the back yard. Bring some sunshine into her life.
Plenty of other ways to use city/county agencies to screw someone over. If she has a pool, even a kiddie pool, call and complain about mosquitoes and say you're worried about West Nile. There might even be an ordinance about how close it can be to a fence. Look her property over for department of buildings/transportation violations, eg, cracks in the sidewalk. Cost her some money to re-do concrete.
Make all calls from pay phones and stay anonymous.
There are also far worse things than these you can do, involving city agencies, but I won't go into them here.
Never take shit from neighbors when you're doing nothing but minding your own business. Get even, and then get ahead.