I realise it has been a while since your post but I have also been looking for some info on a Grace Caven. When I saw your post it reminded me of an entry I had seen on the Dumfries & Galloway council site, 1851 index (
http://www.dumgal.gov.uk/historicalindexes/census.aspx).
For household 18/15 you get these people (plus 4 lodgers):
Name: BOTTOMLEY , Margaret
Address: 1 Mill Street(821):
Parish: Dumfries
Relationship: grand daughter of Catherine Millar
Marital Status:
Occupation:
Age: 5 months
Born: born Dumfries Dms
Household No: 18/15
Name: CAVEN , Grace
Address: 1 Mill Street(821):
Parish: Dumfries
Relationship: daughter of Catherine Millar
Marital Status: unmarried
Occupation: WEAVER woollen
Age: 21
Born: born Kirkpatrick Kbt
Household No: 18/15
Name: FRASER , Margaret
Address: 1 Mill Street(821):
Parish: Dumfries
Relationship: daughter of Catherine Millar
Marital Status: unmarried
Occupation: WEAVER woollen
Age: 17
Born: born Kirkpatrick Kbt
Household No: 18/15
Name: MILLAR , Catherine
Address: 1 Mill Street(821):
Parish: Dumfries
Relationship: head of household
Marital Status: married
Occupation:
Age: 56
Born: born Ireland
Household No: 18/15
My connection is that I have a Margaret Fraser, father = John Fraser, Army Sergeant and supposedly mother = Grace Caven. I thought I had it with this census record but unless there has been a transcription error this Grace can't be the mother of this Margaret Fraser (perhaps the informant at MFs death was confused and Grace was her sister???). But it is possible this Grace is the mother of Margaret Bottomley and so perhaps another child by Grace to your William?
If anyone has the images for the 1851 census I'd be grateful if they could confirm the information in this transcription. Or any information about the family.
Cheers,
Ruth