Yes, I guessed they were Illinois based from looking at the census records for a few hours.
Are you saying this is the wrong family

All the names seem to match

Have you looked at the family on all the census

Were there not more children than you mention

The father Thomas J Dietman may also have been married twice
http://www.rootschat.com/links/0q4h/ Thomas Dietzman and Belle (Laura) in 1900 Marion, Ogle, Illinois
Thomas J Dietzman 39 Belle Dietzman 31
Jessie L Dietzman 13 Bessie B Dietzman 11
Fred F Dietzman 9 William H Dietzman 6
Charles E Dietzman 5 Mable M Dietzman 2
Arthur D Dietzman 1 month
Ornaldo White 55
Birth of Belle Dietman (omitted from your list)
Bessie Belle Deitzman - Birth Date: 5 Aug 1888 - Berlin, Steele, Minnesota
Father's Name: Thomas J. Deitzman and Mother Laura B Deitzman
Thomas Dietman and Belle (Laura) in 1910 Oregon Ward 1, Ogle, Illinois.
Thomas Dietzman 51 Laura Dietzman 40
Mabel M Dietzman 12 Arthur D Dietzman 9
Lela M Dietzman 7 Theodore R Dietzman 5
Frank L Dietzman 2
Thomas Dietzmann - Birth Date: 9 Aug 1858 - Illinois
Death Date: 29 Apr 1916 - Oregon, Oregon Township, Ogle, Illinois - Aged 57 years. General Labourer. Married
Buried 2 May 1916 Oregon
Gender: Male
Father Name: Trouket Dietzmann born Germany and Mother Roselplia Clarke born Wisconsin
In 1920 Thomas Dietzman has died (as shown above) and Laura (widowed) is living with F Lyle Dietzman (thats Frank Lyle) in Dawson, Kidder, North Dakota. Darwin is Arthur Darwin.
Laura B Dietzman 50 (Widowed)
Darwin A Dietzman 19 Lela M Dietzman 17
Theodore R Dietzman 15 F Lyle Dietzman 12 J Guy Dietzman 9 (thats John Guy Dietzman)
East Chicago, Lake, Indiana in 1930 (John Guy goes under Guy and is living with Laura)
Laura Dietzman 60
Mabel Dietzman 31 Theodore Dietzman 26 Guy Dietzman 19
John Guy Dietzman - Birth Date: 5 Oct 1910 - Oregon, Illinois. Aged 22 years. Single. Occupation:- Electrician.
Died 20 May 1933 KeKalb, Illinois
Burial Date: 22 May 1933 DeKalb, Ill - Cemetery Fairview
Street Address: 112 1\2 N 4th St - DeKalb, Ill
Father Name: Thomas J. Dietzman - Buffalo, N Y
Mother Luva B. Edrington - Galesberg, Illinois
Laura Dietzman - [Laura Irington] Birth Date: 25 May 1869 - Galesburg, Illinois - Aged 71 years. Widowed.
Death Date: 30 Jan 1941 DeKalb, DeKalb, Illinois
Burial Date: 1 Feb 1941 DeKalb, DeKalb, Illinois
Father Name: George E. Irington Elaton, Kentucky
and Mother: Elizabeth Piper - Ohio
Spouse Name: T. Dietzman
In 1940 Laura is living with Guy and Bessie Budrow DeKalb, DeKalb, Illinois and described as Mother-In-Law.
Guy H Budrow 54 and Bessie B Budrow 51
Laura B Dietzman 70
Sandra