Hi Music in Me
To answer your question, yes it most definitely is possible for both a parent and sibling to have BPD. My own mother and older sister are both uBPD (undiagnosed BPD).
You are aware that your sister has certain issues and have tried for many years to get her help. Do you feel like your sister acknowledges any of her problems at all? Has she ever perhaps in the past gotten any kind of therapy for her problems?
Your currently are NC with your sister, how long has this been been so? Going NC or not is always a highly personal decision. Whether the NC lasts for an extended period of time or not, I think it is good to use this period to work on your healing and try to find/develop new coping skills. I see you reaching out here as an important step in that direction

The fact that you feel like you are done is a clear sign that after all these years of trying to help your sister, now is a good time to also start taking care of yourself and being mindful of your own well-being.
Whether your sister changes or not, whether she seeks help or not, is ultimately up to her and not something you can control. What you can control is your own behavior and how you respond to your sister.
You also mention your father, do you believe he also has BPD? If you do, what makes you think he might have BPD and when did you start to suspect this?
Feeling hopeless and trapped isn't pleasant at all. I am very sorry you are feeling this way. Having a support network can be invaluable and that's why I'm glad you have a good therapist to help you with what you are going through. I hope this forum will also be a source of support and encouragement for you so you'll feel less hopeless and trapped.
Welcome to bpdfamily