Hi. I am a direct descendent of Jeremiah Parliman. The info you posted about the wives of Jeremiah and his son, James differs slightly from what I have always been told. I am in possession of an heirloom framed "Family Record" which lists the wife of JEREMIAH as Maria D Fuller born 13 Jun 1832. They were married 26 Jan 1858. Their children are Thomas and James and your dates for them match mine.
JAMES' wife was Mary Hester Brown born 30 Jul 1865. They were married 24 May 1888. This much is definitely true as James & Mary were my mother's grandparents and she knew them personally. Mary died 22 May 1945 and James died the following month 16 Jun 1945. My mom said he couldn't live without her.
I have never heard of MARIA CATHERINE MCEWEN or CORNELIA RHINEHART. Do you have any more info? Do you have any info that goes further back than Jeremiah? I know there were ancesters that fought in the Revolutionary War - I would love to go back that far. Also - did you know that the Parliman's have been in this country since the mid 1600's? By the way, what is your relationship?