Wife Katharina Müller, age 29, from Kratzke, second wife
Child #1 Johann Kaspar Kaiser, age 12, probably from first wife
Child #2 Johann Konrad Kaiser, age 5, probably from second wife
Child #3 Barbara Kaiser, age 14, probably from first wife
In the 1798 census, it shows that his father had a second wife. While it doesn't note which wife was the mother of each child, to believe Katharina Müller was the mother of all three children, you would have to believe these things:
Johannes Kaiser's second wife was 17 years younger than he was.
Johannes married his second wife when she was only 14 years old.
She had her first child with him when she was only 15 years old.
While the age difference between the two is likely, it seems improbably that a man over 30 would have married a 14 year old girl. Unless/until I discover otherwise, I am attaching Anna Margaretha (Kaltenberger) Kaiser as the mother of the two older children in the household, Barbara and Johann Kaspar.
Sources
↑The 1775 and 1798 Census of the German Colony on the Volga, Lesnoy Karamysh, also known as Grimm; Published by the American Historical Society of Germans from Russia, Lincoln, Nebraska, USA; Published date: 1995; family #11 in the 1798 census, Johannes Kaiser family.
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DNA Connections
It may be possible to confirm family relationships with Barbara by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Barbara: