I looked at the 1846 certificate and Moses Mulholland senior was a farmer, as was Thomas. Thomas was living in Derrygortenay. So it looks as though he was helping his father on the family farm.
Whilst Thomas may well have been Presbyterian, the ceremony was in the Church of Ireland. Since tradition was to marry in the bride’s church, that tells you Jane was probably Church of Ireland and so if you want to trace her family, those would be the records to focus on. Generally after marrying, the bride would then attend her husband’s church. So their children were probably baptised in a Presbyterian church.
Moses Mulholland is listed in the tithe applotment records for Derrygortenea in 1825. So he was a farmer then:
http://www.cotyroneireland.com/tithe/desertcreat.html
Griffiths Valuation for 1859 lists Moses Mulholland on plots 12 & 13 in Derrygortenea. That was a total of 32 acres. The farmhouse was on plot 13. Today that’s on the Thornhill Rd, near the junction with the Dungogoran Rd, a mile or two east of Pomeroy.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
Moses is deleted from the valuation records in 1862. He was replaced by John Toner. I can’t see a death for Moses Mulholland in the statutory death records which start in 1864. Consequently I’d say he died around 1862, I note a couple of Letitia Mulholland deaths in that general area. One was on 9.7.1874 aged 100, regd in Dungannon. The other was on 16.9.1888 aged 44, in Cookstown (which includes Derrygortanea). Can’t say whether either is your family but it’s not a very common name and you might be interested. You can view the original certificates on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
Statutory birth registration only started in Ireland in 1864 so you won’t find any birth certificates for Thomas & Jane’s 3 children who were born 1846 - 1855. Prior to 1864 you need to rely on church baptism records but not all have survived. The nearest Presbyterian church to Derrygortanea seems to be Sandholes which has baptism records from 1863 and marriages from 1845. There is also a Reformed Presbyterian church at Grange. It has baptisms from 1844, and marriages 1845. Copies of these church records are in PRONI in Belfast. For gravestones, you should try Church of Ireland as well as Presbyterian graveyards. Many Presbyterians used COI graveyards.
The Rock, where brother Moses was born is in the townland of Oughterard. That’s not far from Derrygortenea and so he was likely baptise din the same church as Thomas John. If you want me to try and trace him and his bride Catherine McCann post 1847, let me know what his townland was on the 1847 marriage certificate.
