I believe that Richard may be Richard Whitehouse who married Sarah
Priste at Marston Bigot 26th November 1820. In 1841 he is in Paulton age 64 occ Moulder with Sarah age 63 and an Elizabeth Whitehouse age 17. Richard and Sarah were not bn in County, Elizabeth was.
Also marrying in Marston Bigot were John Whitehouse and Jane
Priston - 18th August 1822, one of the witnesses was a Richard Whitehouse. John and Jane baptised a son Richard 15th October 1825 at Frome, also a daughter Elizabeth 15th July 1823 (abode Bath Street). In 1851 dtr Elizabeth can be found at Stoneham Street, Great Coggeshall, Witham, Essex, unmarried with 2 daughters.
Just wondering if the 2 wives were sisters and one of the surnames incorrectly transcribed, they are similar.

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I am also wondering if Richard's marriage to Sarah was a second marriage for him. Could your William have been a child of the first marriage

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The other family who were resident in Frome were Isaac Whitehouse and Grace Spencer who married in Frome in 1824, they lived in Fromefield though Isaac is not with them in 1841. By 1851 they are in Colchester, Essex. Isaac was born c1803 in West Bromwich, Staffordshire.
occ Master Iron Founder.Richard was a Moulder
John was a Foundryman
Did they all originate in Staffordshire area