Stuck with a closed minded family

So I'm slowly starting to realize that I might be Lesbian, and I totally accept that. I actually feel happy knowing it, and I think I'll be happy when I finally grow into it, and find my own path, but it's my family that I worry about.
They raised me under the assumption that if the same gender lie together, they'll be teased, mocked, bullied, and eventually, killed and will burn in hell. So when I even think about bringing up this thought to my family, I have to be prepared for a HUGE debate that I'm not ready to sit through, especially when the conversation will be about me. My whole family will tear me apart, and I want them to know that this is who I am, and this is who I will be happy being (if that makes sense). But when I hypothetically brought this up to my mother, I already got an earful, and she told me that if I became a lesbian, she would send me to church camp, or rehab until I was cleansed of my sins.
I really need some help with how to bring this up to my family, my friends I don't think will have a problem, but I'm really hurting for advice on how to handle my family, please help me.