Hello Carol
I have completed a family tree for William Armstrong. You will not find Dorthy Jane Armstrong on the 1911 because she was not born until 21.3.1917. I know because she was my Mother. William was born 1879 in Fulford, Yorkshire. In the 1881, 1891 and 1901 census he was living at home. In 1901 he was a Wool Dealer. He married Florence in 1905 in IOM . Florence had an illig. son John N Kneale born 1903. He and Florence had 5 children. Ivy May b 1906, William Arthur b 1908, Thomas Douglas b 1911 (drowned in Douglas Harbour 1924) Leslie Clifford b 1914 and my mother Dorothy Jane b 1917. Florence died in 1923 and william married Margaret Kilgour in 1924. He then sent Leslie and Dorothy to live on a farm near Foxdale. I have a photo of Leslie aged about 11 with Jack and Dennis Clarke at a farm in Ballahowin (on the road from the Braaid to St Marks). Probably this is where Leslie and Dorthy lived. William's occupations were varied. In 1901 a wool dealer, 1905 a miner, 1914 a labourer, 1917 a Private with the Kings Liverpool Regiment, 1923 a Corporation worker and upon his death in 1936 a labourer.
William's father was Samuel Wilson Armstrong b 1855 Fulford Field House, Fulford, Yorks. He was a Farmer. Samuel's father was another William Armstrong b 1817 in Kirk Andrews Cumberland.
All these facts are taken from census forms and copy certificates that I have. I have asked the Corpration in Douglas if they have records of past workers but they do not. Hope this helps.
Doreen