Would it be rude for me to move out?

So i 16f live with my mom and at this point it’s getting unbearable. So for some background my parents are divorced and have been for years i have 3 older brothers in the youngest and the only girl and just a few months ago found out i was adopted. Everything was fine with my mom till i turned about 12 and yes i know your probably thinking it’s because i hit my teenage years and all of that but no it’s not, everything was fine till about march or early april when she started her new job and it’s 2020 and all of the schools are shutting down where i live so i went homeschooled. She started her new job and she traveled a lot and kinda turned it into her own business she was self employed and all of this and i road with her till i was 13 and went back to school for a year and then went homeschooling again and still am and from 14 to 15 i still traveled with her and before you ask me “why would i be complaining we are traveling” we would stay inside the states and that’s perfectly fine with me but we would never stay in a state for more then a day to a day and a half and during that time we where driving or sleeping or stopping at a customers house. So yeah you can see kinda why i didn’t really wanna go. But now i’m 16 and I stay at home and go to work and stuff and hang out with my bf but now just a few days ago my moms husband moved back in with us (he was living in florida for work stuff) The problems happen more when my mom and her husband is home. She yells at me. She’s hit me before. She’s called the cops on me. There’s much much more to but i’ve been thinking about moving in with my dad since he doesn’t do all of that. Would i be in the wrong if i did that? I also have 2 dogs here that are mine and i take care of and pay for and my dad might not let me bring them so if you can help with that please.