All right, sorry about the delay, I was a bit sick!
Here is what I know for sure about William Goodwin/Goodman and (Sarah)* Elizabeth Williams/Goodwin/(Davies?)
*I can no longer seem to find the documents where she was listed as Sarah Elizabeth, but I could swear they existed!
And yes, Williams does come from Birth/Christening data, on all her US-born children's records she is listed as Elizabeth Williams, as here:
Name: William J. Goodwin
Gender: Male
Spouse: Elizabeth Williams
Child: Goodwin
FHL Film Number: 1893712
I am certain this is them in the 1881 Wales census. (Later Rose/Rosannah's birth will be given in her obituary (at least) as the Isle of Anglesey-)
1881 wales census
Name: William Goodwin
Age: 34
Estimated birth year: abt 1847
Relation: Head
Spouse's Name: Elizth. Goodwin
Gender: Male
Where born: Dowlais, Glamorgan, Wales
Civil Parish: Llangynwyd Higher
County/Island: Glamorgan
Country: Wales
Street address: 24 Union Street
Condition as to marriage: Married
Occupation: Rougher In Ironworks
Registration district: Neath
Sub registration district: Margam
ED, institution, or vessel: 10a
Neighbors: View others on page
Piece: 5336
Folio: 24
Page Number: 5
Household Members:
Name Age
William Goodwin 34
Elizth. Goodwin 28
Elizth. Goodwin 9
Rosannah Goodwin 7
Amelia Goodwin 5
William John Goodwin 2
I've read back though and can't see where the Williams name has been confirmed - was this from a baptism or some other record?
A William Goodman married a Sarah Williams or Sarah Davies in Merthyr Tydfil RD in 1874, so Elizabeth & possibly even Rosannah could have been born before they married? I cant find the birth of a Rosannah Goodman but there are several variants of Rosanna Williams around the right time.
There is an Elizabeth Williams of around the right age (18, listed as working in an innhouse) in the home of a David Davies in the 1871 census;
Glamorgan Llanguicke District 15, perhaps that's her?
Here is William Goodwin's USA naturalization data -
Name: William Goodwin
Age: 48
Birth Date: 1848
Birth Place: Wales
Naturalization Date: 1896
Naturalization Place: Cleveland, Cuyahoga, Ohio, United States
FHL Film Number: 1819030
In the 1900 US Census, Elizabeth lists herself as the mother of 12 children total, 9 living, and states her mother and father's birthplace as Wales
William- States birthplace as england, father's as england, mother's as wales, states immigration years as 1882
Elizabeth dies in 1911.
In the 1920 US census, william states the following about his background
Name William Goodwin
Age 74
Birth Year abt 1846
Birthplace England
Immigration Year 1880
Marital Status Widowed
Father's Birthplace England
Mother's Birthplace England
In 1930 William states again that both parents and himself were England-born.
William and Elizabeth's shared grave and related data can be seen here -
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=17968187&ref=acomPlease tell me if you need anything else and I'll try to dig it up, most of what I have is after they came to the USA, of course, it's back in the UK I'm trying to figure out. But I'm happy to sort anything out. Thanks again for all your help!