Thanks very much for your help everyone, I think it's making things a lot clearer.
I found a reference on ancestry (again just a preview as I don't subscribe) that suggested that Elsie Harding died ~2003.
There were also some interesting pictures on ancestry, including one from the wedding of Percival Coan and, presumably, Elsie Harding in 1924:
https://www.ancestry.co.uk/search/collections/1093/?name=percival_Coan&count=50&name_x=s_1There is a sneaky trick you can use to see the full size picture on ancestry - first right click it and choose "vue image" ("vue" is not spelt like that, but rootschat blanks out "vue image" if I spell it correctly!). This will show you something which looks like a thumbnail but is actually the full-sized image being displayed smaller. The name in the address bar will end in "&MaxSide=160". Simply delete the "&MaxSide=160" from the address and the picture will be displayed full-sized!
Anyway, the story here seems to be something like this:
1) 1898 Eva Maud Harding is born.
2) 1902 Elsie Emily Harding is born.
3) 1920 Eva marries Frank Goward.
4) 1924 Elsie marries Percival Coan.
5) 1935/36 Frank Goward dies, Eva moves back to Weymouth.
6) 1935-1939 Elsie dies or separates from Percival.
7) 1935-1939 Eva marries or moves in with Percival Coan and takes his surname.
There are still a few complications involving the various children (e.g. why is the son of Frank Goward and Eva Harding, born in 1925, called William Henry Ellis?).
My connection to this family is also a bit complicated. It involves the possible older brother of Eva and Elsie, born in Weymouth in 1889 and called Harry Charles Harding. He seems to have been adopted by my g.g.grandmother soon after birth and appears in the 1891 and 1901 census as her adopted son. However there is nothing in the family records about him (he would have been my grandfather's uncle) and I wondered whether it was some sort of fostering arrangement rather than a proper adoption which would explain why he kept the surname Harding rather than taking his adopted family's name of Bowdidge. Here is his entry on Family Search (most records attached by me):
https://www.familysearch.org/tree/person/details/G3VC-2X8