Hi Elaine, sent the image offline, but that is definitely the same dwelling:
David Davies, head, wid, 56, farmer, DEN Llansanffraid
Joseph, son, s, 21, farmers son, , DEN, Eglwysfach
Manna E., dau, s, 17, DEN, Eglwysfach
Margaret E., dau, s, 14, DEN, Eglwysfach
Emma, dau, s, 8, Scholar, DEN, Eglwysfach
Diana, serv, s, 16, farm domestic, DEN Llansanffraid
D., son, , 4, DEN Llansanffraid
Owen, son, , 2,DEN Llansanffraid
Although Llanddoget and Llansanffraid aren't far apart, they are most certainly not connected, and I'm pretty sure they don't border each other.
Dianas age in 91 doesn't tie up with 1901 not 1881, but Diana is not a common name in the area (I've transcribed 1891 and 1871 census for Llanrwst, so I know), and I dare say the elder children from 81 have since left home. Although the names don't match up 100%, with 81 and 1901, I'd say this is definitely the right family. Manna E. from 91 is probably Elizabeth in 1901.
I put in a search for Diana Davies, born 1883-1887 in Denbighshire, but the resonse was zero.
A search for Dian* Davies, b 1880-1890 for all of Wales gave 10 responses, but all down south.
I would hazard a guess and say that Diana in 1891 was simply incorrectly emunerated. She should have been 6, not (that would fit in with the ages of the other children. Why else would someone aged 16 be placed between an 8 and a 4 year old? Why else would a servant be placed in the middle of the heads own children?
I'll have a look for David in 71, see what I can find.
D