A quick look at wikipedia shows that the range of the pre-war version of the Junkers JU 52 was about 600 miles. Presumably the reason for the intended stop at Brussels was therefore to refuel, and it seems possible that what made it necessary to land at Ostend despite the fog was the fuel situation rather than the Grand Duchess going into labour, especially with a sea crossing to follow. Of course, if the pilot was low on fuel as well as having someone in labour on board, it was absolutely imperative to land and therefore the pilot made the decision to land at Ostend.
Where had the aircraft taken off from?
Of course, at that time there was no radar and so the aircrew and air traffic control were entirely dependent on the Mark 1 eyeball to avoid obstacles while landing.
Ann