Audrey
Apologies I missed two younger children off the 1891 census (they were on the next sheet):
1891  errata:
Baud, Ernest; Born abt 1884 Rotherham
Baud, John; Born abt 1883 Rotherham 
Pryce appeared to have died in 
1900:Deaths - Baud, Pryce; Age 64 ; 1st Quarter; 1900; Rotherham  Volume 9c Page 513 
They were in 
Whiston, near Rotherham, in 1881.  
You can read all about Whiston here 
http://www.whistonweb.co.uk/heritage/index.htm. There's lots of information on this site about the area and its history, including references to the larger houses (but see cautionary note at the end)
They were captured as Band on the 
1881 census (apologies if you know this already - but I felt if you had you would have flagged up the different potential spellings in the original post):
Whiston, Yorkshire
Pryce Band; Born abt 1837  Sisson, Northamptonshire;
 Head;  
GardenerAnn Band; Born abt 1843  Ratley, Buckinghamshire;  
Wife   Thomas Band; Born abt 1862  Sisson, Northamptonshire;  
GardenerPryce Band; Born abt 1867  Sisson, Northamptonshire; 
Emily Band; Born abt 1869  Sisson, Northamptonshire; 
Andrew Band; Born abt 1871  Sisson, Northamptonshire;
Clara Band; Born abt 1873  Rotherham; 
Fredk. J. Band; Born abt 1877  Rotherham; 
James Band; Born abt 1880  Whiston, Yorkshire
P [no full first name given] Band; Born abt 1879  Whiston, Yorkshire; (Daughter)
I couldn't find any entries in Yorkshire Trade Directories for Pryce Baud.
They were transcribed as Bands in 
1871  too:
1871 – West End, Silverstone  Northamptonshire   
Price Band; Born abt 1837  Silverstone; 
Head; 
NurserymanAnn Band; Born  abt 1841  (indististinct); 
Wife   Thomas Band; Born abt 1862  Silverstone 
Mary Ann Band; Born abt 1866  Silverstone 
Price Band; Born abt 1868  Silverstone 
Emily Band; Born abt 1870  Silverstone 
I did find the 
1861 census though with an even different name:
1861 – West End, Silverstone  Northamptonshire   
Benjamin Bard; Born abt 1794  Silverstone; 
Head  NurserymanMary Bard; Born abt 1795  Silverstone; 
Wife  LacemakerPrice Bard; Born abt 1836  Silverstone; 
Son  NurserymanJohn Bard; Born abt 1854  Silverstone; 
Grandson   I assume John is not Pryce's!  Pryce is shown as single on this census.
There appear to be lots of births and deaths (and marriages) of Bauds (and variants) in Rotherham registration District from the 1870s onwards; eg Annie Baud D 1884 Rotherham Q4 Age 42.  You can try Free BMD or view these on Ancestry.co.uk without paying.
However the marriage of Thomas Benjamin Baud in 1882, Quarter 2, was in Sheffield Registration District, and not Rotherham.  Now Whiston is not far from Sheffield and it would not be that long a pony and trap ride down to Handsworth or Woodhouse, which I believe are in the Sheffield Registration District, but it does make your search for big houses more difficult.   The only big place that springs to mind is Aston Hall (probably about 3 miles away from Whiston).  
There might be a connection between the bride and a big house, so that might be an avenue worth pursuing.  It looks like he married  Emma Hallatt 
or  Harriet Stenton (but don't count on it).  The wedding registration is Sheffield Volume 9c Page 587.
Good luck and I hope all this is helpful.
JULIAN