I presume you have not accessed Charles' marriage certificate? If you have what were the details of his father from that?
If you haven't accessed the marriage it could be in the Irish civil registration and or the overseas section indexes at the Family Records Centre - regimental registers where it may or may not be indexed (in which case not at FRC). The births are indexed but not the marriages. There is an overlapping index which doesn't give regiments called the Army chaplains returns, but this only goes up to 1880 (probably on 1837online overseas section). Otherwise you can try for a search since you know the regiment and roughly where and when the marriage took place. The General Registry Office might be able to produce a marriage certificate if it was an army marriage. However if the marriage took place in a Catholic church then you need to access the marriage through the Irish civil registration system (if in an Anglican church the same applies). They are cheaper than this country because they will do the sensible thing and produce a copy of the microfilmed details of the marriage for half the price of a certified copy.
http://www.groireland.ie/about_us.htmI don't know of any army barracks on Sheppey, but I do know there was a large naval barracks at Sheerness.
There is a family of Hiltons in Stratford showing on the 1871 census (after Charles may have left and been posted out of the country). I cannot find them on the 1861 census.
RG10 1623 folio 183
88 Chapel St. Stratford West Ham Essex
Charles Hilton 48 Tamworth, Staffordshire, Head Married Silk printer
Sarah Hilton 50 Stratford, Essex, Wife Married Weaver
Sarah Hilton 19 Stratford, Essex, Daughter Silk weaver
Joseph Hilton 16 Stratford, Essex, Son Chemicla factory labourer
Arthur Hilton 14 Stratford, Essex, Son Brushmaker
Emma Hilton 11 Stratford, Essex, Daughter
Annie Hilton 9 Stratford, Essex, Daughter
William Hilton 5 Stratford, Essex, Son
Same address for Charles in 1881 and at 94 Chapel Street in 1891. The returns for 1861 may be missing as the enumeration districts on the 1861 index go from 1 to 9 with 4, 6 and 8 missing.
On FreeBMD there is a birth registration for a Charles Hilton at about the right time (there are a lot of Hilton registrations in West Ham district).
HILTON, Charles
Record Type: Births
Quarter: June
Year: 1849
District: West Ham
County: Essex Greater London
Volume: 7
Page: 214
I don't know whether yor Charles Hilton's attestation papers will have survived or not, but I suggest you check for them first. As he was probably ailing by the time of his death he may not be on the muster books in 1900. He may have been transfered off these pay books into military hospital in which case the muster books may not mention him past that point.
Regards
Valda