Flighty can I ask if your dd has been with you long? Don't say if you do not want to.
Re ... having to make it clear that she was not lying about having a brother led to us feeling that there was no other option than to be up front about it with the people we see regularly. I might have done it differently, with hindsight.
I am not sure you could with people who know she has a brother. But if she didn't want to talk about the brother except with really special friends you can be a bit withholding of info!
Re ....had loads of those friendly and usually innocuous questions - "have you just moved to the area?", "where was she at school before?" etc etc. I wasn't really prepared for that and couldn't think of what to say, and I didn't really want to lie to people I was hoping would become new friends.
My husband was the same with ds, he did not like lying. I must be more devious because although I do not like lying I quite like finding slightly devious ways around things!
EG Which school did she go to before?
Oh it was just a local school, not far away, I'd rather not say.
We feel really positive about this one.
We have heard such good things etc.
If you put enough distance between their original question and the chance for a follow up question if might even sound rude of them to ask...
"And why did she move?"
But if they are brave enough or stupid enough to ask, "And why did she move?"
You can be honest and say "We thought this school was better/the best."
Certainly better than going to the school she went to in foster care 100 miles away, is the full truth maybe, but you don't say that!
Also, if you are flattering the school, the school their kid already goes to, the school you both chose, they may well want to say 'Well, yes we really like it." Or they might want to set you straight "Well, some things have not been so great...."
And before you know it you are off on a love feast of this great school you both picked, or you are finding out useful things about what doesn't work well at the school!
I know I sound devious, maybe I should have been a spy!! Too much of a coward! 
Anyone rude enough to ask "Why exactly did your dd leave the school?"
Should get a stern "Because we thought this one was better!"
Or Which school did you say?"
I didn't.
Or What school did you leave?
(Frustrated voice) I'd rather not say!
A Paddington Bear 'hard stare' is optional!
You will probably mentally note this person may well not be the best new friend you might hope for as she or he is unable to keep their big beak out!
Re But now she's at another school and I have no idea how the kids there even know - it's year 4 and upwards, not really children that she has ever had a great deal to do with, and most of them aren't even the older siblings of her friends.
Kids talk, maybe your dd is telling them. This may be a way to explain about not being able to un-tell but also making sure she knows adoption is not anything to be ashamed of!