Well - I have found a few things.
First point is to not totally rely on the spelling of the name as most names varied in spelling dependant on records and the particular scribes at the time.
I have examples of a name being spelt differently in several consecutive records - baptism, marriage, emigration, death.
You can probably also throw in another variation from a Census record or three.
So ....
William VIVIAN married Matilda ROBERTS 17th October 1846 Racine Co., Wisconsin
In 1850 the family was at Raymond, Racine, Wisconsin
Wm VYVYAN, 33, farmer, England
Matilda do., 25, England
Elizabeth do., 3, Wisconsin
Grace do., 1, Wisconsin
Edwin POLLARD, 20, England
This last name 'might' be useful but we know from the marriage record that Williams wife was a Roberts.
In 1860 they were still at Raymond, Racine, Wisconsin
William VYVYAN, 35, farmer, England
Matilda do., 39, England
Elizabeth do., 13, Wisconsin
Grace do., 10, Wisconsin
John do., 8, Wisconsin
William do., 6, Wisconsin
James do., 4, Wisconsin
Matilda do., 1, Wisconsin
Thomas EVANS, 25, farm labourer, England
Another name that may or may not be of help.
The handwriting in the 1870 Census is 'less than perfect'
but the family is still at Raymond.
Wm VYVYAN, 44, male, white, farmer, England
Tilly do., 35, female, white, keeping house, England
Eliza do., 23, female, white, at home, Wisconsin
Grace do., 20, female, white, at home, Wisconsin
John do., 18, male, white, at home, Wisconsin
Wm do., 16, male, white, at home, Wisconsin
James do., 14, male, white, at home, Wisconsin
Tilly do., 13, female, white, at home, Wisconsin
Henry do., 9, male, white, at home, Wisconsin
Geo do., 6, male, white, at home, Wisconsin
I have so far been unable to find William or Matilda in 1880 so, although I will try another search, it would appear they may both have been deceased by this time.
It is also possible that William was deceased and Matilda remarried.
However I have found some of their children who are now at Yorkville, Racine, Wisconsin.
John VYVYAN, white, male, 29, farmer, Wisconsin (both parents born England)
Agnes do., white, female, 29, wife, keeping house, Scotland
William do., white, male, 8, son, Wisconsin
Benjamin do., white, male, 7, son, Wisconsin
Walter do., white, male, 5, son, Wisconsin
John E do., white, male, 1, son, Wisconsin
Matilda do., white, female, 21, sister, keeping house, Wisconsin
William VYVYAN, white, male, 26, butcher, Wisconsin (both parents born England)
Henry do., white, male, 19, brother, butcher, Wisconsin
If you look closely at the 1850, 1860 and 1870 Census you will notice there are some discrepancies in the age of both William and Matilda.
This might make things a little difficult but the problem should not be insurmountable.
1850 - William is 33
1860 - William is 35
1870 - William is 44
1850 - Matilda is 25
1860 - Matilda is 39
1870 - Matilda is 35
Immigration details are also a problem at the moment and I have been unable to find either William or Matilda.
The closest I have found so far for William was an arrival in 1848 with a brother John but that is two years after he married Matilda so would be doubtful.
I will check the 1880 Census again and then maybe take a look at the 1841 Census for England and see what might be found.
CT