Annelaine ... found quite a bit about Jane Ann Davies and the Davies family! I started with the 1901 census and worked from there, but to put things in chronological order here they are. The first few entries become relevant as you read down!
1851 at Cefngwyn, Eglwysbach
William Hughes age 33 (1818) born Eglwysbach, farmer of 20 acres of upland
Catherine Hughes age 32 (1819) born Eglwysbach, his wife
John Hughes age 1 (1850) born Eglwysbach, their son
1861 at Garth, Eglwysbach
Wlliam Hughes age 46 (1815) born Eglwysbach, farmer of 150 acres
Catherine Hughes age 40 (1821) born Eglwysbach,
John Hughes age 11 (1850) their son, born Eglwysbach,
Mary Hughes age 8 (1853) their daughter, born Eglwysbach,
Catherine Hughes age 6 (1855) their daughter, born Eglwysbach,
Thomas Hughes age 4 (1857) their son
1871 at Garth, Cefnycoed, Llanrwst
same family as above but with slight variations on ages
1881 at Ty Newydd, Eglwysbach
Wlliam Hughes age 65 (1816) born Eglwysbach, farmer of 40 acrews
Catherine Hughes age 64 (1817) born Eglwysbach
Mary Hughes age 28 (1853) their daughter, born Eglwysbach
Catherine Hughes age 26 (1855) their daughter, born Eglwysbach, occupation given as "Domestic Servant out of Employment"
Mary Catherine Hughes age 4 (1877) their grand-daughter, born Eglwysbach
1881 at Mardir Farm, Glan Conway
Owen Davies age 22 - see previous information - that's how you can tie in with there!
1882 Owen Davies married Catherine Hughes at Llanrwst
1891 at Rectory Cottage, Trefriw
Owen age 32 (1859) a saer (carpenter), born Glan Conway
Catherine age 32 (1859), born Eglwysbach
Hugh age 8 (1883), born Glan Conway
Mary C age 6 (1885), born Llanrwst
Elizabeth E age 2 (1889), born Trefriw
Jane A age 1 (1890), born Trefriw
1901 at Bryn Rodyn, Trefriw we have
Owen age 42 (1859) a wheelwright, born Glan Conway
Catherine age 44 (1857) born Eglwysbach
Hugh age 18 (1883) a wheelwright, born Glan Conway
Mary C age 16 (1885) born Llanrwst
Elizabeth E age 13 (1888) born Trefriw
Jane A age 11 (born 1890) born Trefriw
Gwilym J age 8 (1893) born Trefriw - transcript incorrect as original shows I not J (longhand script writing!)
Gertrude age 5 (1896) born Trefriw
Thomas O age 3 (1898) born Trefriw
1911 at Bryn Pair, Trefriw
Catherine age 52 (1859) a widow and Lodging Housekeeper
Gwilym Iorwerth age 18 (1893) an Aluminium Works Labourer - that would be in Dolgarrog
Thomas Owen age 13 (1898) an errand boy
Margaret Mary age 1 (1910) grand-daughter, born in Llanrwst
1911 at Glasfryn, Trefriw
Hugh age 28 (1883) a carpenter and wheelwright
Margaret age 30 (1881) his wife, born Llanrwst
1911 at Ffrith y Wae, Glan Conway
The home of James and Anne Evans
Gertrude age 14 (1897) their niece born Trefriw, occupation shown as "helping"
Anne is shown with an "e" and born 1863 but could perhaps be the Ann Davies at Mardir Farm age 10 in 1871 then Owen would be her brother, and so Gertrude would be a niece.
1911 at Grassendale, Mostyn Avenue, Llandudno
Elizabeth Ellen age 23 (1888) born Trefriw, a General Domestic Servant for Walter Richard Kempson, the owner of apartments
I cannot find Jane Ann Davies in 1911 but guess she got married - to a William Rogerson ?
Cefngwyn, Garth and Ty Newydd are all fairly close to each other, alongside the road to Llyn Syberi, Tal-y-Cafn.
More pieces for your jigsaw puzzle!
Big coincidence when I researched that and I thought we would end up related!!! Your line has a Catherine Hughes living in Ty Newydd, Eglwysbach - so does mine! However, my Catherine Hughes was born 1839 and there on both 1841 and 1851 census - she was my great-grandmother.
Dave