Update:
I will create a separate thread but via a vast number of DNA matches we now know Elizabeths parents.
James McArthur and Jane Adams from Co Tyrone.
James dies before 1864. Jane moves to Partick, Lanark, Scotland and is in the 1871 and 1881 censuses. There are quite a few siblings to Elizabeth we cant account for nor do we have baptisms. Siblings include Mary, John, James, Elizabeth, Samuel, Catherine and David.
Children born in 1832, 1847 and 1849 were baptised in Donagheady, Strabane, though their birth places differed - Leat, Tirkernaghan, and Donagheady. James was described as a carpenter at all baptisms.