I'm not sure that the Prince was being rude but I don't think he showed Mary the same degree of attention or interest that he showed Queen Sylvia. It is
a little 'unusual' that Guillaume greeted Frederick before he acknowledged his wife (almost dismissively?). Maybe it's also a little unusual that Fred went ahead of Mary and greeted Guillaume first
Whereas When the King and Queen of Sweden approached Guillaume, King Carl Gustaf stepped back and moved his arm forward as Sylvia went ahead. Guillaume immediately kissed Sylvia, then took her hand. And then
bowed to King Carl.
Maybe this is not the place to say it but I found it a little funny that Fred and Guillaume conducted their entire brief conversation in French as Mary stood idly by.