Your wife should bring stuff up with her doctor. Maybe not bringing things up and assuming the doctor knows what he is doing is part of the general symptoms - naivete, trusting, etc.
My main argument is that knowing she is on a 4 hour shift why send her in the first place withoyt a phone call prior to work "you may need to chaperone can you sort out In the event that your hours will maybe be extended today XX has an appointment at 17:30"
YANBU at all.
To have someone out until 23.15 which turned a four hour shift into an eight hour shift is unacceptable. She absolutely should have had advance warning, even so that she could eat an appropriate meal that would have tided her over for six or eight hours, or packed tampons in her bag if she needed to, or made arrangements for children or family.
They clearly don't want to hire enough people to meet the needs of the clients. It is really poor management to put profit before service, but the care sector is one where employees come and go, and the clients are often people who would never complain about anything, so management gets away with shoddy treatment all round..
I hope your wife will join a union asap, and then start logging incidents like this, including lack of OT assessment.