OK, Jean, you've convinced me. Especially the toothless part. Given that Alice Coulthard isn't anywhere in the 1841 census (and believe me, I've looked!) then "Elsie Gouding" is a badly heard and written Alice Coulthard living with her daughter Jane Goulding.

On to the other daughter Mary in 1851, I think Alice is there with her. This is what I wrote in my last message re this:

"1851 census at 41 Terrace Mile End, Liverpool HO107/2176 825 pg 18 #70
Peter BEATTIE, Head Mar 38 Labourer, b Cockermouth
Mary BEATTIE, Wife Mar 48 Labourer Wife, b Isle of Man
Anne BEATTIE, Daur U 13 Labourer Daur, b Cockermouth
2 lodgers
Alice COULTER, Mother of Peter Beattie, Wid 81, b Isle of Man
This latter person Alice Coulter "Mother of Peter Beattie" is interesting because her name is very close to "Alice Coulthard" mother of Mary. Same age and place of birth too. But this Alice is with her son James. It's almost too much of a coincidence but I don't know what to make of it."

It says Alice Coulter is the mother of Peter Beattie, but the IGI has this baptism:
Peter BEATTY 17 Mar 1813 All Saints, Cockermouth, Cumberland s/o Ann BEATTY.
So I now think Alice Coulter is Alice Coulthard mother of Mary Beattie.

Somewhere back in this thread we also have Alice Coulthard living with her son James in 1851, so she is in two places at once. I've seen this a few times before and probably means she's visiting between the two of them.

'Tis an interesting lot of people.