Actually, I will make a clarification. I'm not an attorney. I have no legal background at all. I was one of those parents you are describing.
I left a very abusive marriage with less than $200 to my name. I ended up in a women's shelter, afraid for my life and afraid for the lives of my daughters. I had to walk into the court system for the first time in my life and learn how to represent myself. I am not an anomaly. These stories are all over.
I am a very strong, resilient person, but for so many survivors, when they are so beaten down by domestic abuse and coercive control, they crumble. They don't have the ability to do what I did. A huge problem in our system is that there are very few resources for survivors.