My father was a John Joseph Mulhern, as well. In my research I found another John Joseph Mulhern who died 12/11/1900, age 18 of a cerebral tumor, pulmonary comgestion. His mother was Maggie Mulhern. They were from Tullyearl.
My Mulhern's went to Co Mayo and may have left in 1796. There is a book entitled Catholics Emigrating from Ulster (1796) to Mayo, written in 1958, pp 17-50. I have yet to see this but it may shed light on some Mulhern's in Mayo originally from Donegal.
From the death records Elizabeth Mulhern, widow, born around 1780, died 1874 (age 94)of Tullyearl.I have a phototat copy of her death cert (short form)and am happy to send it on to anyone who thinks they may be related. I also have Terence Mulhern, Portnason, died age 91 in 1872, Sarah mulherin Derryherk, age 90, died 1873, widow, Susan Doogan, present at death, Catherine Mulherin, age 90, died in 1890, widow of Griff (?), son Pat Mulherin, present at death.Rose Mulhern, age 90, died 1867, widow, Ardfarne, John Mulhern present at death, Millie Mulhern, spinter, age 98, Owenboy, died 1892 and Sibby Mulheran, spinster, mendicant who died in workhouse in 1867 at age 80 in Ballina, Mayo and Ann Mulheron, Eslengort (?)Crossmolina, Mayo, age 97, died 1885, son Micael present at death, also death certs for Sarah Mulhern, servant on Letterncevoge, Crossmolina dsitrict, Ballina registrar district, Mayo, age 75 years in 1885. Also Bridget Mulhearn, Boyhallagh (same as Boholla?), died 1879, spinster, age 34(7?)and a few others in the Crossmolina area.