Should I move out and go to the homeless shelter or should I stay and put up with it?

I have two small sons and I live at home with my mom, I am 24 years old, my sister lives here also she is 21, I am a single parent and I am working a temporary job. I receive help from social service that is how I am surviving. My mom always kick me out of her house me and my kids I know that I am too old to be still living here but I am, she fusses at me constantly and she tells me and my children that she hates us. What should I do? I have a friend that lives in another state and she told me about some shelters up there I could stay at with my children, and maybe I could have a better chance? What should I do?