The Atkinsons were quiet a well-known milling family in Cumbria [Ref: Davies-Shiel, Mike (1978) Watermills of Cumbria, Clapham: Dalesman Books - (O/P)] and I have encountered them whilst researching my own milling ancestors (Robinsons & Clarks).
Dalemain Mill I have also encountered, as one of the Robinsons was there (possibly as an assistant) in about 1860 - possibly a bit later. Indeed - I came across this thread because I was researching Dalemain!
Several of my family also moved to Canada between 1890/1910.
I'll keep my eyes open for any reference to Atkinsons.
Andy