I'm going to take my neighbor's cat to a shelter
Why are you thinking about taking your neighbor's cat to a shelter?
I hate her and the has threatened my dog for barking.
While it's understandable that you were upset at your neighbor's threat to your dog, it's wrong for you to retaliate and try to dump off your neighbor's cat off at the animal shelter. Your neighbor's cat has nothing to do with your dispute with your neighbor and should be left alone. Instead of trying to seek revenge on your neighbor, you should try to get along better and reach a compromise regarding the noise that your dog makes.
I can't stand people who want war so they are just going to get it.
You both need to be adults and take care of your own pets. Some people find barking dogs really annoying you should be more considerate.