I have seen the photos you've mentioned, jackie, and looked at them carefully as well as the one you've posted. The pin shows a Diana in a car doesn't it, arriving at Crathie Church. In that one, she appears, almost definitely, to be wearing the same hat and a light coloured outfit as in the cloak photo.
Royals, especially Diana, varied/vary their outfits for church and therefore she wouldn't have put that particular outfit on for Church on the 23rd of August or any other later date.
Therefore, I am 99% sure that on the 16th August Diana did wear that particular hat and outfit for Church at Balmoral, and again am 99% sure, though I have no documentary evidence to prove it (sorry!) that, when she got out of the Church it proved to be very cold and windy (more than possible in Scotland even in August) and that therefore a member of staff ran up to give her the cloak to wear over her thin, summery clothes. Diana then just happened to be photographed as the Royal party left the Church and walked to the cars taking them back to Balmoral.
Jmo, but I'm sure I'm correct!