Your Mom sounds like my Mom. She treated me like her personal servant all my life-I was responsible for folding ALL family laundry at the age of 3. With every year that passed, I got handed more maid services to do. By 11 I did ALL housework. My Mom didn't work at a job or at home&it didn't matter if I had homework-getting my chores done was always first. Didn't matter if I'd had a bad day or was sick-I HAD to do my chores or she'd scream&yell&call me every name in the book&start smacking, kicking&punching me around. My Dad knew this was going on&often joined in once he got home from work. I was their personal slave&punching bag. When they finally divorced I never heard from my Dad until 4 years later when my Mom left me homeless&penniless. She took every cent of every paycheck I got and I had to resort to stealing to feed myself. Dad did help, but blamed me for everything-why didn't I have a better paying job? Why didn't I know her lease was up? She never told me until I had 2 weeks to find a place to live&I'd just gotten a job in a right to work state(which means no full time jobs with decent pay or benefits). A lot of places wouldn't hire me because I didn't have a car&was not able to come to work in 10 minutes whenever they deemed it necessary to call me in because someone else didn't show up for their shift after I'd already worked an 8 hour shift. My Mom abandoned me after my folks divorced. There was a roof over my head, but no food&often no utilities-I wasn't old enough to legally work yet. She spent all of her time going to bars to pick up men to bring home or if she had a boyfriend, she'd stay at his house all of the time. She'd come home once a week&I never knew when that would be&if the house wasn't spotless she'd beat me. She'd call me every 1/2 hour to make sure I hadn't gone anywhere or had any friends over. She didn't buy food&besides cleaning the house she never was at, she expected me to do her boyfriend's laundry too. When it came to school clothes-I bought everything at Goodwill-she'd give me $10&say "Buy some new school clothes&don't buy those second hand rags you get from God knows where." Even back in the 80's-you couldn'y buy anything but underwear or socks for $10.
I know exactly how you feel&unfortunately unless you're getting beaten up&aren't too afraid to report it-you're not going to see much change if your Mom, Dad&sister won't stick up for you once in a while. I know it sucks-but I know how the system works-they don't care unless there's provable physical abuse.
Keep your chin up, you're not 13 forever&once you graduate, get the Hell out of there&don't have anything to do with any of them ever again. It's the only way that's worked for me. Not cheerful advice, but advice nonetheless. Take care of YOU-maybe report what's going on to a trusted teacher, friend's parent, or a school counselor. I was a punk rocker&nobody gave a damn about me&I'm still here. You'll get through it-it's not going to be fair, fun or comfortable-but just make sure they know-you don't need them&their cr*p anymore the first chance you get to leave. Try to do well in school so you can earn scholarships&grants&make something of yourself-don't be an EVERY TIME LOSER like me.