I don't want my parents to surprise my twin sister with a visit for our birthday
I can't believe you said that. Why don't you want them to come?
I don't want her to end up in a situation that she wasn't ready for.
Some people simply don't like surprises, and that's fine. Have a talk with your parents about it and inform them.
Now I'm wishing I had been a better brother to her.
I think things will work out better if your parents know ahead of time. Can you tell me why both of you live away from them? Did you go to the same school or something?