How do I help my mother with my dementia ridden father when she is constantly yelling and raging every day at me?

My mom suggested I live with her, my dad and my grandson to help my mom manage a three bedroom house, care for my dementia ridden father that also had a stroke, care for my 14 yr old grandson as well. My mom has been showing signs of her health showing signs of weakness especially with my dad staying up all hours of the night, recently she fell again and this time fractured her back! She is very independent and stubborn and refuses to let me stay up at night with my dad. She has never slept longer then 3 hours a night since her 30's. Now she is showing signs of extreme anger and is very explosive. I moved here 5 days ago and every day is the same. I have tried to help by suggesting she call for some help but she says she doesn't have the energy. I help with the housework and she will sleep more often during the day. Even though I am doing everything I can it still isn't enough. I feel like I'm an intruder. Now she is being very emotionally abusive towards me and when I try to say no you can't treat me like this she stone walls me or says she doesn't remember what she said.

I know she is exhausted but I will not accept her treating me this way! She still drives and handles everything including yard work and when things break down, but now instead of dealing with it she rages. She also is treating me like a child and says I peer with my grandson!!

She can be very kind and loving but if anything goes wrong as living in an older home does she rages. If I try to say something positive she doesn't want to hear it. Last night she said that our living arrangement wasn't a good idea after all. Worst of all I'm in the basement at 10 pm with nothing but a chair a light and my computer, along with my bedroom. :( Any suggestions would be appreciated. Thank you.