Working on the knowledge that a child's birth certificate or record would have his mother's surname on it. I looked for the birth record of any of their children.
I found a birth record for Francis, aged 16 on the 1901 census. (I only did this because I have a lot of Truesdales in my tree!)
Would you believe, this is what it says:
date of birth 31.1. 1884
date of baptism 9.06.1884
Francis Trusdale (note, no e)
father: Robert Trusdale, shoemaker
mother Sarah - no surname given!
Seapatrick Church of Ireland
So this is a baptism record, not a civil record
You would have to get his birth certificate, or that of any of their other children, to find the mother's surname.
Hope this helps, or have I got the wrong end of the stick?
RosemaryJoan