This is a shot in the dark, but I'll put it forward as a possibility so that a Joughin researcher can either give it some credence, or refute it. I'm wondering whether your Emily b circa 1831 Braddan might be Emily Joughin.

As you've already discovered, the usual methods for finding the name of a spouse/mother seem to draw a blank. So, since Emily is an unusual surname for 1831, I tried a search in the 1851 census using "Emily no surname, b 1826-1836 Braddan. ( Emily Keig/Kegg appears in all the censuses from 1861 onwards as b Braddan, with a consistent age each time suggesting a birth year if 1831)

The 1851 IOM search didn't show any likely Emily with the right year of birth or parish, so I tried 1851 England and found an Emily Joughan:

1851
Lancashire, Preston 2h/38
Emily Joughan serv unm 19 house servant b Douglas
in household of William Livesay, newspaper proprietor, and Jane nee Gick (m Braddan 1838)

and an extracted baptism for an Emily Joughin in the IGI 28thAug 1831, parents James Joughin and Cathe Crow.

I believe that she may be the E Joughan in this 1841 household of James Joughin and Margaret Crow:

1841
St Ann 1/1
Halfway House
James Joughan 40 publican
Margaret 45
James 14
Robert 12
E 9
Margaret 7
***************

This same family in 1851:

Conchan 7/13
James Joughan head mar 53 miller b Andreas
Margaret wife 57 b Christ (is that Lezayre?)
Margaret dau unm 17 b Braddan
******************

and:

1861
Conchan 7/52
Drumgold St
James Joughan head mar 63 miller b Andreas
Margaret wife 40 b Lonan
Emily gr dau 9 b Douglas
Robert son 1 b Douglas
*********************
(Margaret Joughin nee Crow died in Feb 1858, and James then married Margaret Christian shortly afterwards.)

So please can a Joughin researcher tell us what happened to the "E Joughin age 9 in 1841". Did she marry someone else so she can be eliminated as a possible wife of Edward Keig?

Jean C