Emancipation: Moving in with My Grandmother

My question involves juvenile law in the State of: North Carolina so heres the situation. I am 16 ( june 25 2015) i want to move out badly. I have since i was 9 . I love my mom she is amazing but she has really bad mood swings and makes me feel like another nothing. She loves my brother though. Hes 14, her and him along with her fiance eat supper together and go fishing. They have a great time and seem so happy. I just want to be a part of that but when i try something goes wrong. My great grandmother as I i could stay with her, my mom at first was angry and it hurt her by it also hurt me.. we love each other but i cant live with her. Ive only been 4 monthes clean and when im at home i feel useless and get extremly depressed. My mom said that if she let me stay she could be charged with abandonment charges. Im not sure if thats true or not. Also if we all (me, my grandmother and mom) sigh and do a written agreement to me staying wih my grandmother will that be enough? Is that considered consent? What can i do? Please help me. Im not one of these teens that wants to leave because my mom wont buy me the newest clothes, or we dont eat out every night, or to be with a guy. I want to further my education and try my hardest to excellence in classes and become an entrepreneur. Its become a dream of mine but living with my mom i could never quite reach it. Please someone help i need a answer badly.

Emancipation: Moving in with My Grandmother