As the veteran of 2 C-sections I have to agree. Long distance trips would have been a "No thank you." for the first month or so. This would mean a long train or car ride for both mother and child.Oh, I agree it's not really a good idea to take a newborn out of its routine and schlep it up to the Back O Beyond, for all of the reasons you state, and as I said, albeit jokingly, Balmoral is not exactly the place I'd want to take my own baby - but I'm serious about that.
Also, isn't Balmoral a bit distant from decent medical care? A newborn can't fly due to their ears - must wait about 8 weeks or so.
All in all, if I were a new mother, I'd put my foot down about Balmoral at three weeks, esp. if the birth is a C-section.
And as TLLK mentioned, the soothing sounds of that bagpipe.....
It's a lovely gesture from the Queen, but would anyone be surprised if they said no?