just looking thro some post regarding bethesda and came across this oldie which no one has replied to. Anyway I grew up in Bethesda and can assure you that there are absolutely no hospitals or infirmary anywhere near the village.
From what you wrote im guesssing that the mother grew up in Bryntirion and moved up to Bontuchaf when she got married. A walk from one place to another would take you at least 45 mins
Both Bryntirion and Bontuchaf consist of one row of small cottages and that is it, both these little suburbs are in Bethesda
The quarry hospital which was miles from the village was purely for male use only.
I notice you use the word Inmate as well as being used for a patient it can also mean someone who was poor and had to use the workhouse facility then. The workhouse would have been in Bangor (5 miles away) this is the nearest town to Bethesda
however if you are using the word Inmate as patient in a mental facility the strange thing is there was someone from around Bontuchaf who unfortunately was in denbigh lunatic assylum but i cannot expand on that as u dont mention any names.
if I can help u again with anything ref Bethesda dont hesitate to mail and any welsh translations u are welcomed