You may have all this already:
I assume this is them on the Lady McDonald, arrived 29 October 1856:
Henry HAMMOND, 27, wheelwright, Native place: Norfolk, father's name: Henry, can read and write,
Mary A, 31, parents John and Sarah Cauley, can read and write a little
Elizabeth 12
Harry 4
And this looks like the marriage of Henry and Mary Anne (from Free BMD)
Sep qr 1851, marriage reg at Wayland
HAMMOND Henry = CORLEY Mary Anne
And Elizabeth's birth reg
Jun qr 1843 reg at Wayland 13 371
CAWLEY Elizabeth
1851 census shows Henry 22 as a journeyman wheel wright, lodger with Samuel and Sophia Peake, Caston
Also 1851 - I think this is your Elizabeth, living at Northacre, Caston - all born Caston except those shown
James Corley 50 ag lab b Stow, Norfolk
Sarah Corley 51 wife b Bury, Suffolk
Anne Corley 24 daughter at home
Robt Corley 20 son ag lab
Hannah Corley 84 mother
Elizabeth Corley 8 grandaughter
There are a couple of Mary Ann CORLEY/CAWLEYs in 1851 shown as servants - I had them earlier but can't find them again
So Elizabeth is possibly a step-child for Henry, given her birth registation and the age of Henry at the date of her birth?
There are all kinds of reasons why her mother is named as "Rebecca" on her death cert, remembering that the record is only as accurate as the knowledge of the informant. She was a good age when she died so, as Wivenhoe hs already said, perhaps the person who gave the info got it wrong.
Looks like a death cert is the way to go. You are probably aware that it's cheaper and quicker to get a transcription rather than ordering direct.
Cheers, Judith