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Strive for independence with every fiber of your being. Your family that you live with doesn't love you.
That's why they're dicks to you. They lie and tell you it's "for your own good" or some other bullshit. But really they're afraid to admit that they don't know how to love you... They may not know how to love anyone.
Being grounded for 2/3 of the year every year - when you have no disciplinary or legal troubles - is imprisonment, it is not just punishment. Making you eat vomit is not an important life lesson, it is abuse. A person who openly favors one child over the other doesn't love any of her children, least of all you.
Your brothers learned to love from someone incapable of loving. That's why they are indifferent to your suffering. That's why they only care what you can do for them and feel no obligation to do anything that benefits you.
You can't snap your fingers and be independent. But it is within your grasp if you reach for it. Reach for it with your entire being.
Your dad is reaching out now because you're 18 and he doesn't have to deal with a psycho to get ahold of you anymore. Hold him accountable, but trust his intentions. He's rusty at relating, but let him show you how much he loves you. And use that to remind you of how much the others don't.