There is an Edith Anne Thomas baptised at Tenby in 1874 and an Edith Thomas baptised at Begelly in 1876.
I presume you ancestor was the Thomas Thomas of Llanon, licencee of the Bush Inn (also known as “The hole in the Wall”) in Tenby. The Pub still exists and would even today be well recognized by your ancestor. Old postcards of the street and Pub come up regularly and cheaply on a certain auction site.
I note that Keith Johnson in his book on Pubs of Pembroke, Pembroke Dock, Tenby & South Pembrokeshire, notes that Thomas Thomas was the former Tenby Town Police Superintendent and was landlord at the Bush 1881 to 1891 and has two very good photo’s of the pub in his book (ISBN 1 904396 07 0). I believe the book is still available, although I have no financial benefit/interest in auction sites or book sales.
Given his occupation a search of the 1861 should reveal him as a Policeman in Tenby, although even at this time they where regularly posted between stations, as I know to my cost.
Given that a mrge normally took place in the brides parish, there appears only one mrge on Free BMD that would fit and that is Thomas Thomas to Ann Davies in the Narberth Reg District 3rd Qtr 1856.