Family members can be unpredictable and many will surprise us with acceptance and at least tolerance. Being able to sit down and have a conversation seems best. Be prepared for some to be surprised with initial responses that may suggest confusion. Much depends on the quality of your relationship prior to this conversation. I agree that hearing "the news" from someone else is not in our best interest. No one can share the most accurate and true narrative of your life but YOU. Has the subject of diversity and LGBT people come up before and how did they respond to that?
Please do remember that whatever their reaction, your truth is not dependent on their acceptance and some people do come around, it just takes time to process something they may never have thought about.
Good luck!
