Have you looked on Free BMD yet - all the info can be followed up on that site and with that info you may be able to trace some of the children.
First of all the mother of Ethel Minnie was another Ethel Minnie..Ethel Minnie Ardley as you said, but she married William Cadman as a Tredgett.
Jun 1938 Edmonton Reg. Vol 3a Pg 2828
William C Cadman
Ethel M. Tredgett
(Ethel had been married before)
Dec 1907 Edmonton Vol 3a Pg 887
Ethel Minnie Ardley
Walter Thomas Tredgett
As you said - William's first wife Maud had already died, so I wondered why the delay in marriage - but it seems Ethel's husband didn't die until 1938.
Walter T. Tredgett
died aged 49 yrs
Jun qtr 1938
London City V
Vol 1c pg 4
The births of those three sons you mentioned are also confirmed on Free BMD all Edmonton Reg. also a possible marriage.
Hope this is of some help and hope you are contacted by some descendents.