The messages above are very helpful. I have found a connected person listed here in the 1891 Census. Looking up the relation of the word 'penitent' and 'penitentiary' I was sort of uncertain where this place stood between a "home" and an actual "prison." But I saw that it was under the care of nuns, with the 'St. James' name so I'm guessing the former. Also they all seemed to be training for some occupation, mine was Seamstress. The transcription says they were all "Training in Homo", which I'm not sure what that meant -- for Home type occupations, probably.
My girl turned up 2 years later dancing on the Broadway stage in New York, so the Seamstress thing didn't work in her case.
If anyone does ever find the records, or anything more about it, I hope it will be posted here. It's an odd side-topic.