Well, I have to say this discussion is very funny. I am not Britisch, I don´t understand a lot of what is it like to be royal or what is expected there of a royal.
But, as a mother of 4 children, all born natural, I just can laugh.
First of all, if the Duchess is as down to earth as I think she is, she wants a natural birth, and when there are no medical reasons, no problem, even if you go more than 2 weeks over time. But nobody knows really the due date. So just speculation.
Travelling for a newborn in a big car with - maybe - driver is no stress at all.
If you take care of the baby and it is healthy I don´t see a problem at all - as I said I had 4 of them.
All these theories here are strange to me, but I see all around that common sense is fading all over - it always has be - like this, like that or it is dangerous or false or what ever. I am sorry that the world loses common sense - just because people are afraid of everything, and nobody can accept that things don´t always go the way we want them, so everything has to be controlled. Let nature be nature, be careful and enjoy life.
And if the queen wants to see the baby, they will be able to arrange it - which way ever. If these are alll the problems we have in this world, how lucky.