Hello jgosling and welcome to RootsChat.
Just to narrow things down a little, and clarify a few things:
Clara GLADWIN (dau of Charles), married Joseph SMART (son of Isaac) on 26 June 1902 at Barlborough.
It appears they had the following children:
Dec qtr 1903 Elsie (Chesterfield 7b/842) mmn GLADWIN
Dec qtr 1905 Frances (Worksop 7b/52) mmn GLADWIN
Sep qtr 1908 Harold (Chesterfield 7b/871) mmn GLADWIN (died Jun qtr 1910, Chesterfield 7b/401, aged 2)
Elsie and Frances are with their grandparents Charles and Clara GLADWIN in 1911 at Eckington
I can't see George and Clara in 1911 - do you have them in the census?
Clara LOVATT (SMART crossed out) is on the 1939 register - we're not allowed to post details of the register.
So, presumably something happened to Joseph SMART between 1908 and late 1909 as Nellie was born Mar qtr 1910.
There is a death for a Joseph SMART aged 23 registered at Wigan Dec qtr 1908 (8c/14) - a bit young and a fair way from Eckington, but a possiblity?
Also, it is possible son Harold was also with the grandparents until he died in June qtr 1910, as Clara must have been in Sheffield in Mar qtr 1910 giving birth to Nellie. (Be interesting to see who was the informant on the death certificate.)