Interesting. In the 1891 census, James has his MiL staying - a Maria 
Goodridge, born in St Dogwells.
So naturally you'd look for James marrying a Mary A 
Goodridge - but in 
Dec Q 1883  he appears to marry a 
Sarah Goodridge in the Pembroke District.
Now, in 1881, Maria Goodridge has her daughter 
Sarah in the Household - same age as the Mary A seen in the 1891 census.
If Mary A and Sarah are one and the same, it answers your question as to who was young WJ's mother - but introduces another question  

The 1871 doesnt help - only a younger sibling - Martha - is at home.
1861 seems to show that theres only a Sarah of that age - RG9/Piece: 4159 Folio: 7 Page: 16 Parish of Burton, Pembs. 
William Goodridge 41 Head of Household born Burton: a Dockyard Sawyer
Maria Goodridge 42 Wife born St Dogwells
John Goodridge 17 son born Burton
Sarah Goodridge  11 dau ditto
David Goodridge 9 son ditto
Phebe Goodridge 4 dau ditto
Martha Goodridge 2 dau ditto 
BUT the 1851 has a Mary Ann - HO107/Piece: 2476 Folio: 789 Page: 15 Parish of Llanstadwell 'Little Honeybrough' 
William Goodridg (sic) 31 Head of Household born Pembs, Rosemarket: Dockyard Labourer
Maria Goodridg 32 Wife St Dogwells
Margaret Goodridg 8 dau Burton
John Goodridg 7 son ditto
Stephen Goodridg 4 son ditto
Mary Ann  Goodridg 2 dau born Llanstadwell
Sarah  Goodridg 1 dau ditto 
No deaths 1851 - 1861 in the Pembroke Reg District for a Mary (A) Goodridge, so where was she in 1861 onward ?
1861 - Mary was visiting her sister Margaret, who was in Service in Furzy Park.  RG9/Piece: 4163 Folio: 64 Page: 7
1871 in Service in the Parish of Prendfergast, Haverfordwest - RG10/Piece: 5527 Folio: 91 Page: 16
I'll leave the rest to you up to 1891 etc, but it does look like even tho' James Roberts married Sarah in 1883, by 1891 her sister was the Mistress of the House, given this likely death of a 37 year old Sarah Roberts.
Deaths Sep 1889     Roberts  Sarah  age 37  Pembroke  11a 537 
I believe at that time it wasnt legal to marry your dead wife's sister?
But it does seem to indicate that Sarah was WJ's mother ?