Okay - I did some more digging. To review: here's the household at 12 Back Holgate Street in 1851:
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Richd HUDSON,Head,M,35,Hawker,Manchester Lancashire
Rebecca HUDSON,Wife,M,43,Manchester Lancashire
Betsey HUDSON,Dau,U,16,Hawker,Manchester Lancashire
Mary Ann HUDSON,Dau,U,12,Manchester Lancashire
John WHITEHEAD,Nephew,U,21,Machine Maker,Manchester Lancashire
Mary WELLEBY, Niece,U,23,Weaver,Manchester Lancashire
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However! on 14 April 1851 at Manchester Cathedral, John WHITEHEAD (21, mechanic, son of Benjamin Whitehead) married Mary WILLOUGHBY (23, of 12 Back Holgate Street, daughter of Isaac WILLOUGHBY). The witnesses were Richard and Rebecca HUTCHINSON.
So that seems like the same bunch of people - and it seems that HUTCHINSON might be the real surname, after all....
And the following records might be connected:
On 28 Oct 1860 at St. Thomas in Wigan:
Richard PARKINSON (25, Collier, Bachelor, son of Richard Parkinson, Weaver) married Mary Ann HUTCHINSON (22, Spinster, daughter of Richard HUTCHINSON, Hawker) [The 1871 Census says Mary Ann PARKINSON, 33, weaver, wife of Richard PARKINSON, coal miner, was born in BURY]
On 11 Nov 1838 at St. Luke's in Heywood:
Mary Ann HUTCHINSON (daughter of Richd. HUTCHINSON, weaver [sic] & Becca HUTCHINSON) was baptised.
On 19 Nov 1837 at St. Mary the Virgin in Bury:
Richard HUTCHINSON (Weaver of Wrigley Brook, son of John HUTCHINSON, Weaver) married Rebecca WORTHINGTON (Spinster of Wrigley Brook, daughter of James WORTHINGTON, Weaver)
On 21 Aug 1808 at St. Mary the Virgin, Bury:
Rebekah WORTHINGTON (daughter of James Worthington & Isabella of Heap) was baptised.
....
The reason this intrigues me is that Elizabeth WORTHINGTON of 12 Back Holgate Street (born c1834-35 in Middleton, daughter of James WORTHINGTON, Spinner) married Thomas SMITH on 15 Feb 1852.
I haven’t been able to trace Elizabeth WORTHINGTON (my ggg-grandmother) further back than her 1852 wedding, so I wonder if she was mistakenly enumerated as "Betsey HUDSON" in 1851. But was she really the daughter of James WORTHINGTON and was simply living with her much older sister in 1851, or was she Rebecca WORTHINGTON's daughter, born out of wedlock - or was she something else....?
I welcome any help, thoughts, and/or questions...