I understand the symbolism behind a place of birth, but does it really matter where this baby is born? Isn't it more important an HRH's sense of identity, language, involvement with Sweden, etc?
It would seem silly to give birth in Sweden and then raise it in NYC and have all the perks of HRH. On the other hand, a mere birth in NYC but a strong Swedish identity afterwards seems to be to be far more important.
Madde might be most comfortable giving birth in NY. Her husband works there, they live there, the doctor who knows her history is there. If she has to go to Sweden one month before her due date, and then remain there until they are medically cleared to fly, what is the point? Will that force a separation with her husband? Can he get to Sweden at a moment's notice when the moment arrives - babies can be early. Seems cruel to force that separation.
Personally, if I were Madde, I'd tell the public, "oh yes, I'm giving birth in Sweden - why, I would not think of the child drawing its first breath anywhere else." And then a few months from now, say "Oh dear, oh dear, Doctor has just told me I cannot fly." Wink, wink, Madde...
Although a much easier solution would have been no titles for this child - just little Miss/Master O'Neill. Then the Swedish public would have no say. As long as it's an HRH, and Madde is an HRH, it's their business.