Based on your posting, I doubt if I can give you any information you don't already know.Without actual records from Illinois, Arkansas and Oklahoma, it would be very difficult to confirm the Haney's in those States.And to find the husband of Mary Jane, it "could" be this "Marvel" in Jefferson County in 1870, Illinois; however the family found in 1880 in Arkansas might not even be the same one.The other person posting and I are in Washington State and neither of us should be doing research in these States.
Finding the graves you identified was the easiest part:
The graves of Hester, Annie and Garvin:
--Ruth, I see you have posted an inquiry on this site.
There are several posted family trees on this family; however you need to verify any unsourced information in family trees.
Hester H. Haney is shown as being born in Illinois in 1860(US Census of 1900/1910 and 1920 is used for source, however that age changes).
The 1900 Census for Township 9, Choctaw Nation, Indian Territory
"Hes" Haney, born Mar 1869 in Illinois to both parents born in IL
Amie(as transcribed, "could" be Annie), wife, born Dec 1881 in Arkansas to father born in Alabama, mother in Missouri(Married zero years, so this Annie was not the mother of the children).
Jessie, son, born Nov 1890 in Arkansas
Lillie, dau, born May 1894 in AR
--Previous wife was identified as Martha Ann Weatherford, born 4 Mar 1882 in AR, died 24 Dec 1919 in Monroe, LeFlore Co, OK.
NONE of the family trees re: Hester had information on siblings or parents.
Ira B, dau, Feb 1897.
The 1880 Census of Prairie, Sebastian County, Arkansas
Mary Haney, age 45, born in AR to both parents born in Alabama
Hes, 16, AR
George, 10, AR
"Sis" 6, AR.
"Mahaly" 3, AR.
--no designation if Mary was a widow, separated or divorcee.
Now, the problem:
The 1870 Census of Jefferson County, IL
Marvel(?) M. Haney, farmer
Mary A, 30, housekeeper
William B, 16, son
Marvel M, 15
Hester M, 5, transcribed as Female
Delilah A, 4, Female
Unnamed, age 1/12, Male.
---It appears this Hester is being used in the other family trees as being the one born in Arkansas.OR, this person was a Male, and the other children died, Mary aged 15 years and moved to Oklahoma.Census errors are very common, so this could go either way.The unnamed male "could" be George.This Census was enumerated on 10 July