This should be simple, but there's something about it that doesn't quite fit. I'm not quite sure from your first post, which information came from the relative, and which were your own additions. Was it you who looked in the BRCS Register of Overseas Volunteers, or the relative? And where did the information come from about her joining in 1916?
One real problem is her date of birth. It's is given as 8th December 1899, but the minimum age for nursing VADs to go on overseas service was 23. Even acknowledging that some women knocked a couple of years off their age, it seems extremely unlikely that she could have been in France prior to the Armistice. In the photo dated April 1919 she would still only be nineteen.
The BRCS Register of Overseas Volunteers shows two women of similar names still serving at the Armistice. One is the Isobel Smith you have mentioned in your initial post, but there's a second, Isabel Smith, who was working as an Assistant Cook. Do the relatives know that the one given was their relative, or has the second 'Isabel' been discounted on account of her being a cook?
I have to assume that the photo is definitely known to be the relative's grandmother, and that she was in Rouen in April 1919. The uniforms of BRCS and St. John VADs can be quite hard to separate in photos, and there are no real clues here. The 'officer' appears to be BRCS, but there would probably be some of each at a hospital. However, could I put forward the possibility that Isabel Smith isn't either of the women named in the BRCS Register and actually went to France after the Armistice. If so, then her name wouldn't figure at all in the BRCS Register.
Is the relative certain that the newspaper cutting refers to her grandmother? Could it refer to another Isobel Smith? There was an air-raid on the night of 30/31st May 1918, which destroyed the St. John Ambulance Hospital at Etaples, but clearly a woman with a birth date of December 1899 could not have been working as a VAD in France at that time. But almost every nurse working at hospitals on the French coast during 1917 and 1918 would have been 'under fire' at some time - it was normal, and certainly not a rare occurrrence.
There were many military hospitals in Rouen. This could have been any of them, but unlikely to be No.2 BRCS Hospital which was housed in buildings in the town and not huts.
The problem surrounding the date of birth needs to be confirmed. The grandmother might have dropped her age later in life and was older than she said. If a birth certificate confirms it, then it makes the rest of the information begin to look 'difficult.'
If the relatives haven't already gone in search of her service details (though if not, how do they know she joined in 1916?) the BRCS Archives hold all surviving records for both BRCS and St. John VADs. But it seems likely that there might have been two Isabel/Isobel Smiths living in the same locality, so care needs to be taken.
Regards --- Sue