Apparently no mention of Alberts mother at his death
It was usual to only put the name of the person who reported the death
I think you have confused 2 completely different families here and need to buy copies of the 1915 and the 1918 marriages. The Beatrice Drury you mentioned only married William Smith - not William E Smith
You have Albert born in 1920 to Emily (nee Pratt) and William E Smith
The William Smith/Beatrice Drury marriage was in 1918 so there is no way it is the same William marrying twice. How could Emily give birth to Albert in 1920 if she was dead and William was re-married to Beatrice???
William Smith is a very common name but Edden as a middle name isn't.
A copy of the Pratt/Smith marriage cert will show Williams full names and his fathers name and occupation
The Drury/Smith marriage cert will only show William but will give his fathers name and occupation
Marriages Dec 1918
Beatrice H Drury to William Smith Leicester 7a 509