I'm sometimes asked who "owns" a story and who "gets to write" a story with multiple players, some of whom may not want the story to be written.
Obviously, this is complex territory and there is no one answer. But something that might be helpful is the simple acknowledgment that excavating a story (ie. beginning to write and work on it) is not the same as having it published and read by millions of people. And you do not need to seek anyone's permission to begin to write and work on your story in the privacy of your own computer (or notebook).
Your story is not the definitive family history. It's your version of events as you lived and remember them. And the only person who can tell THAT story is you.
You do not have to worry RIGHT NOW about what will happen when/if it's published or who might be upset if it becomes a New York Times bestseller or what the legal implications might be, or any other thousand scenarios that can keep you from STARTING to write.
And I will almost guarantee that the story you begin to write is not the one you will end up with (particularly if you want to write your story WELL). You do not need to 'be a writer' to write your story. You just need honesty. And words.