I went through something similar with my dad, to whom academe is a mystery. When I moved 12 hours away for work, he was heartbroken and didn't understand why I couldn't get a job as a secretary or teaching highschool with my MA in English Composition. I'm the first one in my family to go to college, and they don't always understand. I'm sorry you're going through this; I know how it feels.
Let's be pragmatic for a minute. Our field is absurdly competitive. You may not find a job when you graduate, and if you do find a job, it may not be one that pays a livable wage. This means that you'll want to go to school that gives you the best chance of finding work after graduate school. That also means that if you earn a PhD in English, it helps to be okay with the idea of moving far away to get a job. Sometimes people luck out and find a job, and if they're incredibly lucky, it's close to home, but that's rare. No matter what, your family's may want to adjust to the idea of you living somewhere far away if they want you to be (a) self-sufficient, and ( equipped with resources to allow you to help them out in the future. It sounds like they just don't entirely understand that; I'm sure they want the best for you.
For what it's worth, three years' after I moved away, my dad has forgiven me, and I've been able to help my little brother and mom out of a few financial scrapes because I took this job, so he's come around. It's not awesome being far away, but working here has opened doors and made options available that will allow me to some day live closer to my family again. Good luck making the decision that works best for you.