@no2rbo,
Start making your plans to escape. Save money, investigate getting roommates (colleges are great places to get this info), and consider how you can continue attending college if you have to pay the entire bill, if you are not doing so already.
If it'll be too difficult to pay for everything yourself while also paying rent, then make sure you sign up for summer school and do your best to graduate as early as you can. College will only get more expensive, and this gives you the jump on any rate increases. Look at graduating as being something that is nonnegotiable.
Study after study shows you make something like $1 million more (or even more) over the course of your career if you've got the sheepskin. This is regardless of choice of major or career.
Talk to your twin and even your little sister about walking the dog in the mornings. Pay them or do their chores for them if you have to. The dog is being used as a pawn and it's not fair to an animal that cannot understand what is going on.
It's not just unfair when this happens. It's borderline animal cruelty.
Your mother has… issues. That's a nice word for it. She sounds like a narcissist. You don't say how old she is, but it is possible for people in their 40s to get dementia, and that can make a person aggressive. I say this not to excuse her behavior at all, but more in an effort to attempt to explain it.
But
I am not a doctor.
You need to protect yourself and your dog, and your little sister if you have the mental wherewithal to do so, because she's also innocent in all of this. If you think things are bad for you, they could potentially end up being a lot worse for her. Girls get an entirely different set of expectations thrown upon us at an early age, and it doesn't get any better when we get older—you just graduate to even more impossible expectations (the garbage that women have to constantly deal with is well-catalogued in
this song).
But
let's get back to you. Your current situation is untenable. You will need to get out of it, as quickly as you can and as well as you can. It's obvious your mother won't help you end this nonsense. But maybe your father will, even if it's just him slipping you a few bucks every now and then.
Your extended family may also be of some help. A favorite uncle or aunt may allow you to live with them over the summer (and if you can take summer classes online, then that would be ideal). A cousin might have a spare bed you can use if you get an apartment. Another might have a pickup and could help you move. Grandparents could conceivably be able to help with something like 529 money for college, if they aren't already.
I can fairly well guarantee that your mother's family knows about her behaviors.
So they will understand why you are coming to them, if you decide to go that route.
I know that depression (again, IANAD) can make you feel paralyzed, like there's no way to fix your problems. But depression is a liar. There are things you can do, and there are probably a lot of people who would love to help you if you would only ask. I hope for only the best for you.