Hi
Thank you for your PM. We are discouraged from using PM's as communication unless discussing living people or sensitive issues so I will reply on here so that others can see what is being said.
You doubt that the death I found for Ada was his wife because of the age difference between Ada & Ernest. You also query whether there was a child of the marriage.
As they married in 1917 in Hamilton (presumably Scotland

) a copy of the marriage if it can be located should give more information on Ada. The child may also have been born in Scotland so will not appear on freebmd (english records) but you should be able to locate a birth certificate on Scotlands people if the birth took place there.
The death certificate of Ernest may be worth purchasing in case the 'informant' details are helpful but if he died in hospital they may not be a relation. As you have an address in Malvern electoral registers may name his wife ( & possible child after they reach the age to vote) There is no child mentioned on his service records.
I can only suggest that the 1944 death was his wife Ada going by the name on death on the register, there is always the chance that it is her and the age has been transcribed to the GRO index incorrectly. I can see no other suitable entries on the gro index but she may have returned to Hamilton after Ernest died in which case her death would be registered there.