To the OP: I've added approx date of birth and wife for Ole Christian Tidemann below (may help identify him), along with names of some of his descendants (not a complete list).
About Clara Marie: Is Tideman her maiden name or married name? There's a Tidemann family in Minnehaha County, South Dakota, who are from Norway. I'm not entirely sure which Clara is yours. Here's one (birth year is off, but she's in Minnehaha county, South Dakota):
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Ti...;
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Ole Christian Tidemann born ca 1811 ? Gram, Frøs, Haderslev, Denmark;
married
Johanna Marie Jensdatter b ca 1816
Ole Christian and Johanne Marie CHILDREN
1) August Friedrich Tiedemann born about 1837 in Gram, Frøs, Haderslev, Denmark
2) Ann Kirstine Tidemann
3) Hanna
4) Jens Christian Tidemann born 21 Oct 1842 Denmark; d Concord, Dixon, Nebr.
to USA 1881, married
Maria Nissen - their children
* Catherine Kate Marie Tidemann (married Niels Christensen)
* Johanna Hanna Marie Tidemann (married Thomas Mullivan)
* Sine Tidemann b 1867
* Anna Christine Tidemann (married name Nelsen)
* Hans Tidemann (married Ida Josephine Nelson, son Oscar Tidemann b 1898)
* Mary Tidemann (married David Edward French)
* Fredricka Tiedeman (married Lee Elmer Evans, children Elmer, Benjamin, Eunice)
Not a complete list
5) Ann Tidemann born 19 Feb 1853, Thiset, Gram, Haderslev, Denmark
married in Denmark to Sanke Detlef Nielsen - their children
* Anna Katherine Nielsen (married Fred John Bluhm, children Jack, Thelma, Faye)
* Carl Christian Nielsen (married Margaret Laurenzen)
* Ole Christian Nielsen
* Mary Johanna Nielsen (married John Bensen)
* Margaret Nielsen (married Rolla Ernst Pelham, son Robert)
* John Nielsen
* Ella Nielsen (married Andrew Wallace Hogg)
* Alvin Nielsen (married Ethel Mae Hall, children Robert, Donald, Marvin)
Not a complete list
6) Hansene Tidemann b 30 July 1856 Denmark
married Johan Sofus Ferdinandsen Husum - two children
** Sofus V Husum (married Julia Arnold, their child Harry Husum)
** Louise Husum (married Armenes Ryner, Dow Starr, Martin Heiney)
to USA 1885
married Peter Nissen - children
** John Nissen
** Ole Nissen (married Helen Anderson)
** August Nissen (married Olga Jensen, their children Donald, James, Joann)
** Dora Nissen (married Chris Dahl, children Victor, Lester, Darrel, Wilma; Wilma m Lund)
** Esther Nissen (married Hans Henry Poulsen, children Ellen and Louise)
** Dagmar Nissen (married Bruce Pelham, children Esther and Margaret)
** Nina Nissen (married Henry Frederick Specht, child Frances)
Not a complete list
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1834 Danish Census
Haderslev, Frøs, Gram (Kongerigsk), Thiset Bye, 2, et Huus, 2, FT-1834, C6771
Ole Christian Tidemann age 23, unmarried, living and working as "Tjenestefolk" i.e. hired hand on the Hans Sorensen farm
1840 Danish Census
Haderslev, Frøs, Gram (Kongerigsk), Gram Sogn, Thiset Bye, et Huus, 2, FT-1840, C7986
Ole Christian Tidemann age 29, married, working as "Tjenestekarl," hired help, same farm
1845
Haderslev, Frøs, Gram, Thiset Bye, et Huus, 2, FT-1845, C0088
Ole Christian Tidemann 34 married, "Tjenestekarl," same farm, birthplace here in Gram
1845 Johanne is still enumerated separately.
1845
Haderslev, Frøs, Gram, Dorf Thieset Kirchsp. Gramm. Ausbauern, Hufenparcele, 38 F 1, FT-1845, C0088
Johanne Marie Tiedemann 29 Gift ihr Mann dient bei einem Schackenburger?? Bröndum A. Ripen
August Friedrich Tiedemann 8 Ugift ihre Kinder Thieset
Jens Christian Tiedemann 3 Ugift ihre Kinder Thieset
Anne Tiedemann 6 Ugift ihre Kinder Thieset
Ludewig Hansen 1 Ugift ihre Kinder Thieset
The family shown together in 1860.
1860
Haderslev, Frøs, Gram (Slesvigsk), Jenning, Et Hus, 34 (4), FT-1860, D7050
Ole Christian Thidemann 49 Gift Husfader. Daglønner Gram Sogn, Haderslev Amt
Johanne Marie Thidemann. f. Jensen 45 Gift Hans Hustru Brøndum Sogn, Ribe Amt
August Frederik Thidemann 22 Ugift Deres Barn Gram Sogn, Haderslev Amt
Anne Kirstine Thidemann 14 Ugift Deres Barn Gram Sogn, Haderslev Amt
Hanne Thidemann 11 Ugift Deres Barn Gram Sogn, Haderslev Amt
Anne Thidemann 7 Ugift Deres Barn Gram Sogn, Haderslev Amt
Hansine Thidemann 4 Ugift Deres Barn Gram Sogn, Haderslev Amt
This is not complete and not authoritative - just a start to maybe help cousins find your post.