I have been trying desparately to find information on my gt grandfather Thomas Cook - to no avail!!However, whilst searching for info on Carlyon, I came across your posting.
Information from my father:
Amy Cook born 1902 c (dated from photo taken in 1906) married a Jack (?) Carlyon.According to my father they had 2 children Ronald (now deceased) and Jocelyn who married a geoge Smith and moved to Kent.
One of Thomas's other children, Thomas Cook born 1897c was also killed in the Sengyhydd pit diaster.All this seems similar to what you are posting.