I've done a bit of research on your Ggrandmother Esther's family.
As I mentioned there are birth registrations for three possible Esther Holliday's which fit time and place wise.
As your Esther specifies that she is born in Oughterside in the 1901 census, looking at the 1881 census, the other Esthers give different places of birth, so I think this might be your Esther with her widowed mother:
1881
Adams Ghyll
Plumbland
Mary Holliday wid 52 farmer of 3 acres b Cumberland Dean
Jonathan Jackson son unmar 27 coal miner b Jallentire(?) [so Mary has a son from a previous marriage

]
Martha Holliday daur 12 scholar b Oughterside
Esther daur 10 b OughtersideSarah A daur 8 b Plumbland.
RG11/5179/45/20
Estimating Esther's year of birth as 1871, I wondered if she made it onto the 1871 census. Sure enough, she did - just.

She is with both parents and a complicated 'blended' family (as I believe they are called now

).
1871
Oughtertides,
Oughterside
Dannial [sic] Holliday head mar 42 coal miner b Aspatria
Mary wife 42 b Dean
Jonathan Jackson stepson 17 coal miner b Tallintin (?)
Robert Monkhouse stepson 13 coal miner b Gilcruse(?)
Joseph Holliday son 12 coal miner b Wigton
Jane Holliday daur scholar b Hayton
Mary Monkhouse stepdaur 9 b Willeruse(?)
Jonathan Holiday son 6 b Aspatria
Martha Holiday daur 3 b Aspatria
Esther Holiday 3 months b AspatriaRG10/5245/13/22
This looks fairly complicated to unravel. It looks like Mary may have been married twice before she married Daniel. The most important thing for you to know is that Esther's parents are Daniel and Mary, and they are your gggrandparents.
Here is their marriage:
Mar 1/4 1867
Holliday Daniel
Mo
unkhouse [sic] Mary
Cockermouth 10b 644
Mary's previous marriage:
Sept 1/4 1857
Jackson Mary
Monkhouse Thomas
Cockermouth 10b 577
At this stage I don't know if Jonathan Jackson was illegitimate and Jackson was Mary's maiden name. Though looking at her birth estimate of 1829, she would have been 27 when she had Jonathan in 1854, so until we have further proof, we can assume that she was married to Mr Jackson, but we don't know what her maiden name is. There are quite a lot of Jacksons marrying girls named Mary in a likely timeframe and area prior to 1854 (Jonathan's birth) so the only way to find out for sure is to purchase Jonathan's birth certificate. Unfortuanately there are a couple of options - one in 1853 and one in 1854. But as Mary is your gggrandmother you may wish to do this at some stage, in order to trace her family further back.
I will let you know if I find anything else.
