Hi
This is a long shot as there are so many people with the same names in Wales.
However by searching for the same mother's to children with the names you mention I found that the only one which came up for William 1913, Susy 1915, and Gladys 1919 was PARRY. They were all born in Llanrwst Denbighshire. Then there is a Eurwen J born 1910 in Llanrwst, but parents name not given.
The only thing is Williams birth was the Jul/Sep qtr of 1913 not Oct/Dec as you have it, which could blow the whole theory.
There must have been more than one couple with the names Jones/Parry living in Llanrwst, but these are additional children from parents with those names
Robert O 1912, Blodwen 1913, Myfanwy 1914, Catherine F 1914, Naomi 1916, Thomas J 1916, Trefor 1916, Hugh H 1917, Mary E 1919.
Looking at the census returns Eurwen appears to be the dau of John Jones 1873 Anglesey a blacksmith and Ann 1874 Capel Garmon Llanrwst, who had children Annie 1900 William 1904, John 1908 and Eurwen Jane 1900 all in Llanrwst reg district. They are on 1901 census ref RG13 5241 36 12.
There is a marriage of John Jones and Ann Parry O/D 1897 Bangor ref 11b 866
It may not mean anything but Bangor is the biggest town/city between Llanrwst and Anglesey
I hope this may give something to work on, but eveything needs verifying, as it could be totally wrong
dave