Hi Chris,
I cannot see Richard's Baptism c1850 in FoD records, or the witness Susan Hatton (his mother?) either for sure. Do you have any other leads please ?

From GlosBMD:

Birth Details

Child Surname Child Forename Father Surname Mother Surname Mother's Former Name Year District Office Register Entry
HATTON Richard Francis HATTON HATTON THOMAS 1850 Forest of Dean Monmouth, Coleford 7 198

Searching for Hatton?Morse births in GlosBMD give the following, altho of course they may NOT be yours, however these are the ONLY ones in their whole county database and the dates & Office Location fit the marriage nicely.

Child Surname Child Forename Father Surname Mother Surname Mother's Former Name Year District Office Register Entry
HATTON Bessie, HATTON HATTON MORSE 1883 Forest of Dean Monmouth, Coleford 41 198
HATTON Kate, HATTON HATTON MORSE 1884 Forest of Dean Monmouth, Coleford 42 190
HATTON Minnie, HATTON HATTON MORSE 1885 Forest of Dean Monmouth, Coleford 43 180
HATTON Stanley, HATTON HATTON MORSE 1886 Forest of Dean Monmouth, Coleford 44 184
HATTON Albert, HATTON HATTON MORSE 1889 Forest of Dean Monmouth, Coleford 46 435
HATTON Harry, HATTON HATTON MORSE 1891 Forest of Dean Monmouth, Coleford 48 164
HATTON Annie, HATTON HATTON MORSE 1893 Forest of Dean Monmouth, Coleford 50 59
HATTON Eliza, HATTON HATTON MORSE 1894 Forest of Dean Monmouth, Coleford 52 8
HATTON Frank, HATTON HATTON MORSE 1896 Forest of Dean Monmouth, Coleford 53 116
HATTON Richard, HATTON HATTON MORSE 1898 Forest of Dean Monmouth, Coleford 54 439

I'm struggling to find any of these Baptisms in FoD PRs.
However it suggests there should be some of these still in the area in the 1891 Census, have you searched the WALES Census too ?

Searching this forum gives this prior thread wrt another Richard Hatton and a Sarah (note the above named witness!). This thread is a tangled one !
http://forum.forest-of-dean.net/index.php?id=1607

Given the apparent "casual" nature of the family within this prior thread, and the apparent reluctance of your couple to Baptise their Children, I do wonder if your couple and those in this prior thread are linked quite closely...

???

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Pre marriage Richard and his father Richard may be found in the 1861 Census for Yorkley, judging from this site's Census search page. Sorry but I dont know with certainty how to compile their exact Household from the 28 Hattons resident in 1861 Yorkley;
http://www.forest-of-dean.net/index.php/census-search

I think this is a household group ?
1861 Census, Yorkley
Surname First Name Age Place Box Piece Folio Schedule
HATTON Charlotte 13 Yorkley 15 3981 79 36
HATTON Henry 5 Yorkley 15 3981 79 36
HATTON John 3 Yorkley 15 3981 79 36
HATTON Mary Ann 35 Yorkley 15 3981 79 36
HATTON Richard 37 Yorkley 15 3981 79 36
HATTON Richard 11 Yorkley 15 3981 79 36
HATTON Ruth 8 Yorkley 15 3981 79 36
HATTON Susan 1 Yorkley 15 3981 79 36

Also on LDS / Family Search;

"England and Wales Census, 1861"
Name: Richard Hatton
Event Type: Census
Event Date: 1861
Gender: Male
Age: 11
Relationship to Head of Household: Son
Birthplace: West Dean, Gloucestershire
Schedule Type: Household
Registration District: Monmouth
Sub-District: 1 Coleford
Ecclesiastical Parish: St Pauls
Parish: West Dean
Residence County: Monmouthshire

Which FINALLY gives, also from LDS:

"England and Wales Census, 1881"

Name: Frank Hatton
Age (Original): 30
Gender: Male
Birth Year: 1851
Birthplace: West Dean, Gloucestershire, England
Relationship to Head of Household: Son
Marital Status: Single
Occupation: Coal Miner
Address: St Johns
Event Place: East Dean, Gloucestershire, England
Disability:
Record Type: Household
GS Film number: 1341609
Affiliate Publication Number: RG11
Piece/Folio: 2523 / 54
Page Number: 11
Household Gender Age Birthplace
Head Richard Hatton M 53 West Dean, Gloucestershire, England (a "general labourer")
Wife Mary Ann Hatton F 55 Coleford, Gloucestershire, England
Son Frank Hatton M 30 West Dean, Gloucestershire, England (a "coal miner")
Son John Hatton M 23 West Dean, Gloucestershire, England (a "general labourer")
Daughter Susan Hatton F 21 West Dean, Gloucestershire, England
Grand Son Frank Smith M 3 West Dean, Gloucestershire, England

Which ties in nicely with 1861 above.

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Similarly Eliza seems hard to find wrt her Baptism, is this her Birth from GlosBMD ?

Child Surname Child Forename Father Surname Mother Surname Mother's Former Name Year District Office Register Entry
MORSE Eliza MORSE MORSE MORSE 1854 Forest of Dean Monmouth, Coleford 10 334

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From FreeBMD I think this maybe your Richard, perhaps explaining why he's hard to find in the later Census ??

Surname First name(s) Age District Vol Page
--------------------------------------------------------------------------------
Deaths Sep 1899 (>99%)
--------------------------------------------------------------------------------
Hatton Francis Richard 49 Monmouth 11a 12

I hope this helps a little, sorry I don't have full access to the subscription Census sites.

Many Thanks to all of you!

The Morse's were Non Conformists which is probably why you won't find any baptisms. I must admit I did not think to look on GlosBMD as I felt sure they must have moved away.

Richard using various names got me stumped there!

Thanks again - off to update my tree now.

Kind Regards
Chris