Your mother may not know it or show it, but she is lucky to have such a caring daughter as you. Instead of just getting angry, you are concerned. Me too. It’s possible that your mother is depressed. Yes, I know. Most people think of depression as sad. But some people get irritable and easily set off. It doesn’t sound like there is much that gives your mother satisfaction — even having 4 daughters who are growing up and doing well. My guess is that she is overwhelmed and unable to acknowledge that something is terribly wrong.
You mention a dad but you didn’t talk about whether you have approached him about the situation. You’re right that your younger sister needs protection. So do you. Could you and all your sisters confide in your dad? Perhaps he could talk to your mother about getting some help. Maybe he could offer that both you and your younger sister could stay with him to give your mother a break.
If your dad isn’t someone you trust to help you, please think hard about whether there is another adult who might help your family. Do you have a grandparent or another relative you could ask to help your mom? How about the school guidance counselor?
No kid should feel unsafe in her own home. No kid should feel responsible for the safety of a younger sibling when it’s all she can do to take care of herself. I’m very glad you wrote. Now please follow up and get someone involved who can offer you support and practical help.
I wish you well.