At only 16, you are asking very thoughtful questions. Unfortunately, there are no universal answers. Generally, it is the abuser who has to leave, not the victim. But if the family is totally without resources, it’s true that the state may step in and offer foster care until your mom can get on her feet. If there are relatives who are willing and able to take care of the kids and mom, that’s usually the best option.
Usually women like your mom are afraid to leave for the very reasons you are afraid to call the authorities. They are afraid of the abuser. They are afraid their children will be taken from them. They don’t want their kids to be homeless. They are so beaten down, they don’t have much self-esteem left. Often the abuser has made threats that are truly scary.
In order to help women in these situations, women’s shelters have been set up throughout the US. Here’s the website for shelters in your state. You and your mother could call the shelter in your city to talk about what they have to offer. Usually there is counseling and education for women who are victims of domestic violence. Many centers also maintain safe houses where women and children can stay while things get settled with the abuser and the woman applies for government benefits and looks for work or, in cases like your mom’s, figures out how to manage on her own.
You are a sensitive and caring young woman to write the letter you did. I hope you can encourage your mom to make an appointment with the local center. You all deserve to live without fear.
I wish you all well.