Sorry it has taken us awhile to reply. I checked the main information in our Arn family tree and came up with the following.Since these families tended to be very large, she is likely related to ours in some way. Here is a brief outline of what we have on the Arn family tree related to my husband;
Johannes Arn (born circa 1646 in Switzerland) died May 23, 1702 in Durrn, Germany. He married Katharine Klumpp circa 1685 in Durrn. So, as you can see by these two names, you are likely very definitely related to my husband's family. We have no idea who Joannes Arn's siblings or parents are nor do we know who Katharine Klumpp's parents or siblings are. This is likely where yours fits in with ours.
Johannes Arn and Katharine Klumpp had six children that we know of (there may have been more that we do not know of). The ones we know of were the following:
Juliana (b.c. 1692, Johann Michael b. 1693, Eva b. 1695, Martin b. 1696 (died 1757), Catharina b.c.1698, Anna Barbara b.1701.
My husband's family are descended from the Martin Arn who married a second wife in 1742. His name appears to be Hans Martin and he was born Dec. 28, 1696. He married twice. The first wife was Katharina Schlegel (22 Feb. 1724) but it is from his second wife Regina Catharina (1742)that my husband is descended from. As Hans Martin died in 1757, there must have been another generation down where our Cornelius (Kornelius) fits in as he was not born until May 13, 1795. He married August 8, 1816 to Karoline Wilhelmina Bossert on August 8, 1816. Kornelius had two siblings named Johann Jacob and Daniel.Kornelius/Cornelius was a farmer in Durrn in 1836, a Burgomaster in 1837 in Durrn and in 1850 he emigrated to Canada. He died in Canada in 1866. He had 17 children but 7 died young.
Now here is something interesting. You said that your Mathias Klump married an Ernestine Arn. Well, back in the 17th century, our Hans Martin Arn (who was born 28 Dec. 1696), had a brother Johann Michael who was born 1 October 1693 and married May 10 1718 Anna Barbara Schafer (Johann Michael Arn died in 1760). One of their children was named Ernestina (she was born 1741 and is the youngest of their 10 children that we have listed. Here are the names of all of Johann Michael Arn and Anna Barbara Schafer's children:
Catharine Barbara 1719, Johannes 1721, Margaretha 1722, Anna Rosina 1726, Anna Eva 1728, Johann Michael 1730, Maria Salome 1732, Jacob Fredericke 1734, Daniel 1736 and then Ernestina 1741. So perhaps this Ernestina is your ancestor!
Hope this is not too confusing and that it helps somewhat!
Susan and Bob Arn
London Ontario Canada