You running at her chasing her angrily is not the same as her attacking one of your children. Your children do not discipline her or try to. It sounds like you think this may mean she will attack unprovoked or just out of the blue. Why do you think this?
Sounds like you had a bad night. First its sounds like she attacked you because she was scared. You said you were chasng her and screaming. Thats enough to scare anyone. Has she shown any kind of aggression before? I dont think this one incident means she is going to attack anyone unprovoked. You are not the only one who would like to get rid of your animals sometimes. I wanted to send Elie to the pound after what she did to a little dog at the dog park. Your only human. Relax. My suggestion is to take a little time to yourself and calm down. Nothing good will come from making decisions when your angry.
"Ok...well, she has been kissing my hands and slouching around like she is trying to say sorry." Then she probably is trying to say sorry. Most dogs do not like to attack their owner, and they will try their best to let you know they are sorry if they do. Once when I reached down next to my dog's head for something and she was chewing on a toy she bit me (posession aggression). Afterwards she became very submissive and "kissy" towards me even though I hadn't punished her for biting. She knew what she had done was not "right" and she was trying her best to say sorry for it. ~Seij