I had a look in Griffiths Valuation for Dromore c 1860. There were only 4 John McLoughlins listed. 3 of them were not farmers. This was the only farmer but his wife was Nancy not Mary, so unless he had remarried it doesn’t look to be the correct family. Probate abstract from the PRONI wills site. The will itself is on-line. He leaves everything to his wife. No mention of any children.
The Will of John M'Laughlin late of Lettergash County Tyrone Farmer who died 27 November 1886 at same place was proved at Londonderry by Nancy otherwise Anne M'Laughlin of Lettergash the sole Executrix.
Note: M’ is how surnames were originally written in Ireland (and Scotland) before Mc & Mac became more popular.
Birth registration only started in Ireland in 1864. Prior to that we rely on church baptism records. I searched the RC records but did not find Peter’s baptism nor any siblings. Neither did I find his parents marriage.
The statutory records do contain one possible entry of interest. A John McLoughlin was born on 29.5.1865 to a mother whose previous name was Gallagher, and registered in Irvinestown. Irvinestown is in Co Fermanagh but part of its registration area is in Tyrone. (Events in Lettergash would be registered in Irvinestown, for example). So the 1865 birth could be worth looking at. I can’t find it on the irishgenealogy site but it is on the GRONI website. Unfortunately that;s pay to view. £2.50 to see the certificate.
https://geni.nidirect.gov.uk/
There were some McLaughlins farming in Dromore parish in the tithe records (1834) including 1 John who appears to have lived in Dromore village. Presumably his land was nearby.
https://www.irishgenealogyhub.com/tyrone/tithe-applotment-books/parish-…