In looking for this family, I came across this. I think it may be the family you are looking for.
In 1910 census there is a John Gird age 40 b. Ne. and Anna age 26 b. Ne. with two children, Jennie age 5 b. Wy. and Margarette age 1 1/2 years old. In 1920 John is listed a widow in Butler, Ka. living with a brother Frank and his wife Sara. Jennie listed as a niece age 14.
It seemed to me that this is the family so decided to check the Wyoming Archives Newspapers. In the Sheridan Post, Nov. 30, 1917 page 1, is this, Anna Gird was given a judgement and decree of divorce against her husband John Gird. The Girds were married in Sheridan July 15, 1906 and are parents of four children ages range from 3 to 10 years.Mrs Gird secured her divorce on grounds of extreme cruelty and alledged her husband beat, brusied and injured her during the month of July 1916. After that she claims he deserted her and since has refused to live with her.
A summons was made to John Gird whose last known address was El Dorado, Ka. Anna had filed for divorce on 15 Sept. 1917.
July 21, 1905 Sheridan Post . page 8
A marriage lisc. was issued Monday by Co. Clerk to John Gird of Rosebud Co, Montana and Anna Kelly of Crook Co, Wy. Were married by Justice Blackburn. I can't explain the dates are a little different, prob. did not have a correct date for the divorce decree.
In my mind, it would seem that the children, Jennie, Marjorie(Margarette),Jessie and Jackie(John) were the children as mentioned. That when they were divorced, John kept Jennie because she was older and didn't need the care and the other three being younger were placed in a home.The 1920 census says John was a widower, he may or may not have been. Perhaps Anna had died after the divorce and he kept Jennie, placing the younger ones.
There are probably more newspaper articles if you would care to check the Wyoming Newspaper Archive.
Good luck. If I can answer anything else, let me know