Information about Catherine came from the Marquette County Historical Society, J. M. Longyear Research Library. This is a secondary source that identifies Catherine as Catherine Birdsall. There are other sources that identify Catherine as Catherine K. Van Iderstine, so the K may stand for the name King, as you have heard.

There is also a page from the Van Iderstine Family Bible printed in the Detroit Society for Genealogical Research Magazine, Volume 28, Issue 4, Summer 1965 that lists the marriage of Jeremiah P. Van Iderstine to Catherine K. Birdsall, January 1, 1844. Again, this is a secondary record; it is re-typed from the bible information. I have seen the name Catherine spelled with a K as well.

Obits about Jeremiah identified his parents as John Van Iderstine and Elizabeth Pope.