Ah, now Joshua would have been a couple of generations older (born about 1822), and in the 1852 letter I have, his nieces and nephews were via his sisters (so would not have had the name Roylance), so I don't *know* of a direct link, but I'd still bet there is some connection!
My own Roylance connection, in brief: Joshua's sister Sarah Roylance married a guy named William Davenport, and their daughter Hannah Davenport (b.1854) is my great-great grandmother.]
I did take a look just now at the UK 1881 Census (via www.familysearch.org) and I do see a 1 year old Kathleen Roylance (no middle name listed), living at Tipping Brow, Mobberley, Cheshire, England that year. I wonder if that might be your grandmother? That would make her ~25 in 1905, so she is about the right age, at least. In the census, her parents are William and Mary Roylance, both 26 (in 1881) and also living with her is William's widowed mother (also named Mary), then 72 (so born about 1809).
So, I have no idea if this matches what you know about Katheleen, or if it's just someone else with the same name, but thought I would pass it on. Best of luck tracking down the family history!