I understand how painful this is for you. It’s especially difficult to be estranged when from your point of view you’ve done nothing to deserve it. Having repeatedly made contact and been rejected, you are right to try to move on. It’s like shaking the doorknob of a locked door over and over and over. It’s still locked. At some point, it’s time to give up and either find another door or go to another house.
I vote for the latter. I’m sure you’ve talked to your older sister about the situation and tried to address it with your parents. Older sister can’t help. Your parents don’t want to. For whatever reason, your parents can’t figure out to be parents of two. Give up. The door is locked and there isn’t another route in. It’s their loss at this point.
My best suggestion is that you go next door. Actively seek out some older, interesting people who would love to have you as their friend. We all need older people in our lives who think we’re terrific and who love us for who we are. Older people provide wisdom, mentoring, and reassurance that we can get through the next stage. Younger friends provide them with a window into what’s next, energy, and help. The relationship is reciprocal and mutually rewarding.
“What?”, you say. “Find parent surrogates?” Yes. Precisely. You miss having parents. There are lots of interesting, vital, and loving 60 and 70 somethings out there who would love to be your friend. I think if you focus on developing relationships with a few of these people, you will find it less painful to let go of the people you were born to.
I wish you well.