The obituary for Margaret seems to me to be giving the name of the county she came from, because why else add the word county after the place name, in the American way of naming counties? There are only 32 counties in Ireland so it’s usually not too difficult to work out a mis-spelled name. To me, I’d say that was a mis-spelling for the county of Cavan.
If she came from Cavan, and her family were farmers, then there are only 2 Barnett families listed in Griffiths Valuation for that county in 1857. The two farms were side by side in the townland of Cornanurney, and were farmed by John & Thomas Barnett. (who were most probably related). There were still 2 farms there in the 1901 census:http://www.census.nationalarchives.ie/pages/1901/Cavan/Tully...http://www.census.nationalarchives.ie/pages/1901/Cavan/Tully...
Cornanurney is a few miles south of Cootehill. The church tithe (tax) records for Cornanurney in 1833 record that the 2 farms were being farmed by John & David Barnett respectively. You might want to check out the local Presbyterian Church records for that area, to find George & Mgts baptisms. (The records are most unlikely to be on-line and you would likely need to go to PRONI in Belfast to get a copy). You could also check for gravestones in the local graveyards. (Presbyterians quite often used Church of Ireland graveyards, so check those too). You might need to make enquiries to find which church they attended, but I’d guess it was one of the two Presbyterian churches in Cootehill. Cootehill 1st Presbyterian church’s records only go back to 1870 (presumably earlier records have been lost) but the 2nd Presbyterian church’s records start in 1822, so you have to hope that was the one the families used.
If the family were Presbyterian then it’d be reasonable to assume they were of Scottish origin, and their ancestors probably came to Ireland in the 1600s as a part of the Plantation of Ulster.
It’s hard to say what George’s death says. The first word does look like West, but the second doesn’t look anything like Meath.
There were two Barnett properties listed in Griffiths for 1854 in Westmeath. One was in Tyrrelspass, the other in the main street of the town of Kilbeggan. No Barnetts in the tithe records for that county, nor in the 1901 census.
I’d be inclined to investigate the Cavan families first.