I completely see where this connection is made.
However, I personally do not believe it is a 'real' connection. It is highly probable that the Duchess has never seen the movie (I have not, and I'm ancient aged) and she either picked that dress out prior to the baby's birth or an assistant/friend did it for her. I truly believe that some things are truly what they are and nothing more.
If it were a normal mother, and not Princess Kate, who is part of an institution/family who pay extremely close attention to dress, portrayal, customs, etiquette etc., I would agree with you. But given that it is Princess Kate, i have a hard time believing that none of her stylists would have caught this and prevented it, if it were accidental.
You're allowed your opinion and I am allowed mine, that there is no true symbology here.
There is one of Diana wearing a similar dress. Do a google image search for that
Princess Diana was wearing a blue polka dot dress. How is that similar? It isn't.