The children's baptisms of an a soldier serving in the army overseas are often found in the overseas section of the General Register Office index at the Family Records Centre (baptised by the regimental chaplain), only usually baptised locally if the soldier was not Church of England or no regimental chaplain was available. Those records can be searched online at 1837online. The records begin in 1761 and the GRO will issue certificates for any reference found. They have the sort of information found on baptisms not on births.
Tasmanian BMDs can be searched here (this early parish records)
http://portal.archives.tas.gov.au/menu.aspx?detail=1&type=P&id=314567Not sure but this seems to be indicating a marriage for these Rothwell parents - John and Mary Anne in Hobart in 1840, but children baptised 1840-1845 which would fit the time span.
439862 ROTHWELL MARY 1840
439874 ROTHWELL WILLIAM 1842
439847 ROTHWELL JANE 1843
439858 ROTHWELL LOUISA 1845
3 baptised Hobart, William baptised Green Ponds.
Baptisms in India if not held by the GRO are held by the British Library (plus burials).
The National Archives has no record of a James Molineux receiving an army pension pre 1854 except one born in Warwickshire discharged 1853 aged 39.
No Rothwell/Molineux marriage on FreeBMD. Overseas/army marriages again will be held in the GRO overseas index.
The son born at sea in 1850 was still alive on the 1851 census
Deaths of FreeBMD
Deaths Jun 1851
Rothwell John Wigan 21 61[79]
Deaths Sep 1852
Rothwell John Wigan 8c 46
ROTHWELL John Wigan 8c 56
You might be able to persuade Wigan registry office to check the ages at death and only issue you a death certificate if they find a man of the a right age, preferably an army pensioner.
There are also two James Molineux deaths registered in Wigna pre 1861.
Regards
Valda