found more on Samuel FWaite, was son of a policeman in 1871, living shirenewton, then 1881 in Caldicot father has left police and both are working on the railway as contractors. Father Mattew died 1919 Chepstow at 85.
Welsh info seems a bit limited, you may need to travel to Wales to research at National library, (check on google for details)
I was wondering if they eloped to Scotland to marry, as she was underage, so Scottish records another area to explore.
Was Samuel in the Military too? there was/is a barracks building in the area, I think, just over the Severn bridge, so he could have joined up. Death cert would give you some info, especially who notified.
Think you need to find birth regn of Matthew Eliza and Edith to work out who was living where. That may help find Thomas too.
good luck.