On Joseph Twist's Will in 1883 proved to be his Housekeeper not his wife.   
Her two sons are living there - John 'Twist' aged 14yrs. William 'Twist' aged 12yrs. (plenty found out about William).   
Emma died in 1859 and her death certificate says Emma Aston aged 46yrs.    
 
I am presuming Aston was her birth name and not a previous married name. 
Could her two children be living with family members in 1841? 
Could she have named her first born John after her father  
 There is this baptism
Emma Aston Birth 21 Mar 1816
Baptism 15 Apr 1816 St. Martins, Birmingham, Warwick
Father 
John, occ 
carpenter & joiner Mother   
MaryHave you ruled out this Emma?
Hospital Street, Upper Court, St George, Birmingham, Warwickshire
Emma   Twist   1813   Warwickshire occ carder
Elizabeth           1841   Warwickshire not found a birth mmn Aston
Do you have 
Joseph Twist on the 1841 census?
Can you give more details of Emma's death who was the informant ? Was it a family member?
On 1851 census  -  Emma shown living as 'wife' with Joseph Twist in Birmingham.  So named as Emma Twist.  Being 34yrs.  No place of birth recorded.   
On the 1851 census I see they have a son Joseph Twist - Is this his birth & do you have the birth certificate?
TWIST, JOSEPH   
mmn ASTONGRO Reference: 1849  M Quarter in BIRMINGHAM  Volume 16  Page 338
Is this Joseph & his father in 1861?
1861 Piece   2120
Folio   97
Page number   32
Kings Norton   
Joseph Twist   40   Head 
occ Horsedealer Joseph Twist   13   Son
both pob dittoed as Birmingham
There's also this birth entry
TWIST, CHARLES   
mmn ASTONGRO Reference: 
1851  J Quarter in BIRMINGHAM  Volume 16  Page 361
and this 1871 census entry 
1871 Piece   3079
Folio   123
Page number   28
Kings Norton   
Joseph Twist   55   Head Bn Birmn occ  Inte... 

 op…. 
Joseph Twist   22   Son        ditto occ horse dealerCharles Twist   18   Son bn Kings Norton occ ditto
Samuel Twist   16   Son                 ditto  occ ditto
1861 census 
Charles age 10 and 
Samuel Twist age 8 are boarding with a 
William & Eliza Dedicoat Not found a birth entry for Samuel to confirm mmn but there is this possible marriage same occupation as 1871 census but he has a middle name and his father's occ is different  
Samuel Gunn Twist Age 21, occ 
horse dealerFather   
Joseph Twist, 
occ builderSpouse   Mary Ann Wright
Married 7 Oct 1872 Birmingham, Bishop Ryder, Warwickshire
There is a Joseph Twist 
occ builder born Birmingham c 1821 married to Caroline bn 1838 on 1881 census living Grove Road Kings Norton