neuroticnicky, re choice....I"m with you on that one (depending on the 11 year old, and their track record of knowing what's right for themselves, I suppose).
We looked at state and private, without dd, then those we would have been ok with we looked at again with her - and we let her choose where she wanted to apply. Our only condition was that she apply to more than one. Then, once we knew what her options were, we let her choose.
In the event, she applied to one state and one private, got both and chose the private. I would have chosen the state, for myself, and dh the private, but both of us are fine with her choice and she is very clear in her own mind - as she usually is (and it usually pays off when we listen to her on something like this).
You know yourselves and your dd, I would back your intuition and ignore the relatives 