The details in the 1841 and 1851 census returns suggest it is the same William Edwards.
1841 has William married to Sarah, the name is distinct. They have children who include John, aged 2 and Richard aged 1 month. The family is living at Ffynnon Lon... William is shown as aged 30, Sarah, 36.
In the 1851, William is shown as aged 40, married to Sophia, aged 42. Their chidlren include John, aged 12 and Richard, aged 10. The family are living in Bryndengan (??)
The names and ages of John and Richard, suggest this is the same family.
It appears that Sarah died between 1841 and 1851. I have checked BMD but there are a number of deaths registered for a Sarah Edwards in that period. The registration should have been in Holywell district.
Some of the records for Ysceifiog are on Freereg but I couldn't find anything for him, or them, on there.
http://www.freereg.org.uk/Have you found them on the 1861, or later census returns? There may be more clues there.
The problem with genealogy in the Ysceifiog area is that there were so few surnames and it is very difficult deciding who is the right person. I have this problem myself with a 4xgt grandmother by the name of Mary Williams born 1790. I looked at the parish registers to find a total of 5 possible Mary Williams all born there at that time. I shall never know who was "my" Mary.
Jo.