This is Jennet in the 1871 Census and possibly John living separately he could have been looking for work.

1871 Wales Census about Jennett Owens
Name: Jennett Owens
Age: 29
Estimated Birth Year: abt 1842
Relation: Head
Gender: Female
Where born: Pembroke, Pembrokeshire, Wales
Civil parish: St Mary Pembroke
Ecclesiastical parish: St Mary
Town: Pembroke
County/Island: Pembrokeshire
Country: Wales
Registration district: Pembroke
Sub-registration district: Pembroke
ED, institution, or vessel: 2
Household schedule number: 67a
Piece: 5515
Folio: 28
Page Number: 13
Household Members:
Name Age
Jennett Owens 29 (Lab wife)
Mary J Owens 7
Ellen Owens 5
John Owens 2

address 67a Middle Street, Orange Gardens

This is a possible for John

1871 Wales Census about John Owen
Name: John Owen
Age: 32
Estimated Birth Year: abt 1839
Relation: Lodger
Gender: Male
Where born: H West, Pembrokeshire, Wales
Civil parish: Llanstadwell
County/Island: Pembrokeshire
Country: Wales
Registration district: Pembroke
Sub-registration district: Roose
ED, institution, or vessel: 2a
Household schedule number: 196
Piece: 5521
Folio: 51
Page Number: 48
Household Members:
Name Age
John Driver 29 Mariner
Fanny Driver 26
Frances Mary Driver 7
Richard Hall Driver 5
Beatrice Driver 3
Lewis Henry Driver 4 Months
William Morgan 49 Lodger
>>>>>>John Owen 32 Lodger Labourer

address Cambrian Street

Marriage for John Owens & Jennet Rogers

Surname First name(s) District Vol Page
Marriages Sep 1861 (>99%)
OWENS John Haverfordwest 11a 865
Rogers Jennet Haverfordwest 11a 865

You should be able to find the children's births on www.freebmd.org.uk. A copy of the Marriage certificate will give you more information on John & Jennet and their parents.

happy hunting