Hi,
Sounds like a totally normal family reaction. Don't worry. They haven't thrown you out. They obviously love you. They are in shock.
Have you ever been in either physical or emotional shock? It isn't horror movie shock. It is a full release of hormone and chemokines etc that affect every part of your body.
For your family to be told that there 'son' is now their daughter and proceeding with it is a total and complete mind and emotional shock. Remember, and we all forget this, WE know for ages that we are TG, we slowly accept it, try and understand it. We talk to people, including here. Then we make the decision; for our life. Then we tell Mum and Dad and Sister; Oh BTW I'm TG hope you can cope. In future female pronouns and I'm to be called XX.
Real easy for them?
Total knew experience for them. Most know nothing about TG. Why should they?
How to proceed? Don't know every situation is different.
I do not know your circumstance, do you live at home? Do you have your own place and visit?
OK take your sister out to lunch or dinner as two sisters at a meal. Lots of questions. Lots of talk. She loves you and you love her and get it together. My sisters had NO problems accepting me and I don't recall any threads when sisters do not accept. You have to be brutally honest. it will be difficult but she needs to totally trust you and you her.
You and your sister take or make dinner together as women. You are comfortable with being you, your sister supports you. Talk the female talk as you all make dinner, again honesty is paramount. You can never let these people not trust you ever again.
Dad doesn't matter, he will accept what the woman say, he may gruff up, but most males just want to be fed and have a happy family.
Hope this is of some use.