I have William and Catherine's marriage certificate but there is no mention of William's mother so her name on the Catholic register is a breakthrough 😁
William and Catherine's first daughter was Mary so I suspected she may have been named after William's mother.
The burial of Mary McKay in Ardwick is definitely my next line of enquiry.
Glad to have been of some help
Instant digital image available from GRO if you want to take a chance - cost £3.00
MCKAY, MARY 71
GRO Reference: 1873 D Quarter in CHORLTON Volume 08C Page 448
Edit to add
I've been looking to see if I can find Mary on 1871 census but no luck yet
