Eric, that would have been Saint Gerards, it is on the same complex as the other homes, but was always a hospital based service, as you rightly say, run by the nuns. It was a sanatorium and latterly an orthopaedic hospital, but sadly was closed in 1998. Last time I was there,the buildings still remained but I believe they are to be demolished and the land sold - I will check that out later.
The reason I know about it was that I worked there from 1991 to 1996 and loved it,the nuns ruled with a rod of iron but were so kind.
We used to take in respite care patients from the North Warwickshire community to enable their carers to have a break and picked them up in a red minibus, dubbed the "Happy Bus" by the patients. Most of them enjoyed their stay as the grounds and outlook was beautiful.
We also used to look after poorly priests from around Birmingham before they moved on to longer term care.
It was alovely place to work and the girls who were still there when it closed still have regular reunions.
Sue