She is showing on the 1851 Census at
www.dumgal.gov.uk/historicalindexes/census.aspxEMERSON Elizabeth, head of household, widow, age 53, b, Stranraer
EMERSON Elizabeth, unmarried, age 24, b. England
Address: McCulloch Place, within Stranraer, Parish INCH
The fourth entry might also be relevant, as the John age 14 also shows an England birth.
Just key in EMERSON on the search page and you will get four entries including the two above.
You should also try searching the site for EMMERSON. There are eleven entries some of which could fit in age as children to Caleb and Elizabeth, also showing an England birth place.
On IGI there is only one submitted entry for an Alexader b. 1825
Regards.
Monica