Hi
Sorry for not getting back to you sooner. As William is a mariner, chances are he would be at sea often, and therefore would not be on a census.
I think I’ve cracked it for you. Wouldn't unduly worry about the Wood/Woods
1871 Wales census *8 Kingtons Court, St Mary, Cardiff
RG10; Piece: 5360; Folio: 8; Page: 10;
Elizabeth Wood Head 43 WIDOW Seamstress born Bridgewater, Somerset
Charles A Son Un 19 Timber Labourer born Bridgewater, Somerset
Henry Son 13 scholar born Bridgewater, Somerset
MARY A dau 10 Born Cardiff, Glam
1861 Scott Street, St Mary, Cardiff
RG9; Piece: 4033; Folio: 25; Page: 44;
Elizabeth Wood Head MARRIED 33 born Bridgewater, Somerset
Ellen dau 13 scholar born Bridgewater, Somerset
William son 10 scholar born Bridgewater, Somerset
Charles son 8 born Bridgewater, Somerset
John son 6 born Bridgewater, Somerset
Henry son 3 born Bridgewater, Somerset
MARY A dau 1 month born Cardiff, Glam
1851 Honeysuckle Alley??, Bridgewater, Somerset
HO107; Piece: 1925; Folio: 89; Page: 48;
Elizabeth Wood WIFE (Head) Mar 23 MARINERS WIFE born Bridgewater,
Ellen dau 3 born Bridgewater, Somerset
William son 1 born Bridgewater, Somerset
William Wood married Elizabeth 1844 4th quarter
Reg dist Bridgewater Vol 10 Pg 500
This is where I’m stuck - THREE Elizabeth’s on page Elizabeth Fish, Elizabeth Pitman, Elizabeth Shield. Sorry no way I can tell which one he married.
BUT I did find these – perhaps you could order a birth cert?
Ellen Wood born 3rd quarter Reg Bridgewater Vol 10 pg 290
William born 2nd quarter Reg Bridgwater Vol 10 339
I have also found this website link to a Somerset site that will do look ups for you, but knowing the great people on this site, you could try putting the marriage details on the Somerset board and seeing if anyone can find out the information for you.
Have to go now, will have a look for 1891
Looks good to me

Joan