my mom was kinda like that too, she would ground me or take stuff away for the dumbest reasons, and she said i pay the bills, if you dont like it get out. she said that a million times. she would lock me out of the house until i apologized for something rediculous, but only after an hour or two alone outside. first time i got kicked out of the house i was 6, and probably 1 or 2 times a year till i started walking to a friends or whatever. then she got really mad because i left. if i was you and your parents punish you for stupid shit, give them a reason to punish you or get out. my favorite was when she used to throw stuff at me and i'd try and stand in front of something that was hers so when i ducked and she missed it would brake her stuff, then i would laugh at her. then she would have a reason to be mad.
she always told me to get out if i didnt like living there, and made me pay rent of $80 a week as soon as i got my first job. She wouldnt let me get my license while i was at home so just after i turned 18 we had a fight and she told me to get out, i did when she was at work. i packed a box of stuff and went to a friends house. i stayed there for almost two weeks till she finally found out from one of my friends where i was staying. she checked on me and knew i was still going to hs and work, then asked me to come back home. just after i graduated we got in another big fight and she told me to get out if i didnt like it, so i called my dad (hadnt talked to him in like 10 years, practically disowned me and ran away when i was 2) he let me use his car to get my drivers license as my mom wouldnt let me use hers or keep a car at her house. a couple weeks later i bought a really crappy car, packed up all my stuff and moved out when she was at work one day.
hard ass parents suck, but they just make you stronger and someday you wont need them at all, they are just using thier power while you're still there while they can. good luck and get out when you get a chance