The change to "three years dead" does seem to clinch it. Perhaps the "20 years" refers to the writer's own mother, i.e. she meant, "I have no doubt you do miss your dear Mother, for I do [miss mine] even though she has been in the Heavenly House for more than twenty years".
Mary Ann Hawkins and her premarital son William were both born in Yeovil, according to the census, which is where the letter came from. So presumably the writer was a friend or relative of Mary Ann. FreeBMD gives several Mary Ann Hawkins born in Somerset in the right time frame, but none in the Yeovil district. If you want to trace that side of the family further you'll have to get her marriage certificate to see who her father was.
I have now discovered in Ernest James Woods Army documents reference to his siblings, he states he has 2 sisters, Minnie and Kate. As there is no mention of William I think we have to assume he was deceased when these documents were completed in 1902.
William married Ellen Davis in 1898, calling himself William Henry Hawkins Woods. He was still alive in 1911, and had a son called Ernest in 1908, so I would think he was on good terms with his (half?)brother. (James Woods was only about 15 when William was born but I suppose it is possible that he was his father.)
I feel the photo is definitely James Wood with 2 of his 4 children and either his first or second wife.
?? I thought it was Harry Brewer with his wife and two children. There's nothing to indicate James Woods was in the Army. He was over 50 at the start of WW1. His youngest children were the age in the photo in around 1790. Had that style of uniform come in by then.
You've now quoted the name on the back as
Mrs K I Brewer. Does it really say that. I was assuming it was written by Constance Irene Kathleen, who had taken to using only her third and second names... written in 1934 but taken around the time of WW1. But perhaps it was written by her mother, with the I meant to be an E.
David