According to one of the posts in the threads "The children, date range, 1879_1904 when Arthur Thomas Arnold(Thomas) was born. He was sent to live with Charity Brown in Derby". Charity was another one of Elizabeth's Children. I'm questioning where was his father Edwin? but if you have found on the 1911 census, then he was not sent away. It has crossed my mind that Arthur may not have been Edwin's son. Still not any clearer as to Edwin's where abouts at this time.
Also Edwin's Parents (Edwin and Keziah) were still alive, getting on but still alive and I wonder why they did not intervene with the situation concerning the children. Going on research with My Arnold family it was very common for family children to reside with other relatives - who ever had room sort of thing.
I appreciate the time guys i really do