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www.nationalarchives.gov.ukSource of the Baptisms and Marriages is acknowledged as being from the I.G.I. microfiche
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G'day Amanda
This probably duplicates what you already have, but I throw it into the melting pot, just in case.
I believe that you have the widowed mother , 3 daughters & 1 step-daughter at 25 Clarence Square in the 1851 Census ?
I assume that this mother, Susan age 60 in 1851, was the 2nd wife of Charles ? - the 1st being Arabella Smith ?
as Matilda, the step-daughter, was 46 in 1851.
Susan was shown in the 1851 Census as being born in Herefordshire and although the rest is open to interpretation, depending on your eyesight !!,
the census image page place of birth could be viewed as 'Weston' ?
In the I.G.I. in Herefordshire there is a marriage between a Charles Newman and a Susanna Parker in 1812-Jan-06 at Weston under Penyard HEF.
Weston under Penyard is approximately, as the kookaburra ? flies, 20 miles North-West of Stroud and also 20 miles West of Cheltenham.
A stones throw in OZ !!
I know its wrong to assume, but the ages of the 'later' kids appear to tie into this date ?:
Caroline Susan c1817 - a Caroline Susan Newman is shown in the GRO Deaths 1889 March Qtr Cheltenham age 72 ( = b.c1817 )
E J c1823 ( who was this other daughter shown in the 1851 Census ? )
Lucy S c1829 - a Lucy Selina Newman is shown in the GRO Deaths 1910 March Qtr Cheltenham age 80 ( =b.c1830 ) - I wonder if she left a Will ?
The closest Death I can see for Susan / Susannah is a Susannah Newman - Death 1872 March Qtr Cheltenham age 83 ( = b. c1789 )
We know Charles died before the 1851 Census - there are 3 deaths of a Charles at Cheltenham in the GRO indexes from 1837 to 1851
1837- September Qtr, 1848 December Qtr and 1850 June Qtr
Do you have any 1841 Census details ?? If he is alive in 1841 then this narrows it down to 2 Deaths.
Matilda Newman Death 1889 September Qtr Cheltenham age 84 ( = b. c1805 )
I cant find Arabellas death ? if it was before 1866 then the ages do not show in the GRO indexes.
Other bapts. of kids of Charles / Arabella Smith - - all at Stroud GLS
Chas Saml 1798-Jun-28
Henry 1801-Jan-22
Matilda 1805-Jan-01
Helen 1809-Jun-12
At Teresa ? Place, South Hamlet ( ED 5a ) GLS in the 1851 Census - Film 1962 Folio 392 / A
Edward ROBINSON Head Married 56 Paper Merchant b Littledean GLS
Augusta S ROBINSON Wife Married 41 ? ( Enumerator strike-through ) b Cheltenham GLS
Arabela P NEWMAN Visitor Un-married 37 ? ( Enumerator strike-through ) Attorneys daughter b Stroud GLS
Arabela (sic) appears to be one of yours ?, but I wonder about the wife, Augusta S Robinson ?
Can you seek a look up for this marriage ?, it would be nice if there is a connection - hopefully sisters

I was working on the lines of Frederick Augustus Newman and this Augusta

- probably wild speculation ??
Cheers Mike Newman - a small cog in the Newman Name Society