I descend from the Hildebrands of Nevada County. In the book THE HELDEBRAND HERITAGE by Helen Odum Harrell (1980), there are two pages on Margaret Jane Heldebrand, who married Martin Mitchell about 1874. It says Martin was born about 1851 AR and his parents had come from Georgia. Margaret was the 8th childof Daniel Jefferson Heldebrand (who's my great-grandfather) and Daniel's first wife Dorothy Permelia Parnell. Margaret was born 1851 Union County AR & died in the 1940s. Her nickname was Maggie, Mag or Mog, and I have several photos of her and Martin. She was a vivacious, colorful character who lived well into her nineties but never got old.

Margaret & Martin Mitchell had 3 children:
...(1) Thomas Thaddeus Mitchell born 1875, died 1960, married Kansas Lambert (both buried at Pleasant Grove Cemetery, 9 miles north of El Dorado on Hwy 15 in Union Co AR). They had 7 children.
...(2) Louis Wilmar Mitchell born 1878, died 1935, married Nannie Prim (born buried Friendship Methodist Church Cemetery, west of El Dorado between El Dorado & Cairo, 1.4 miles south of Hwy 82). They had 4 children.
...(3) Lula Mitchell, married #1 Johnny Harris & #2 Oscar McCleskey. They had 2 children. (I have contact info on a descendant of Lula's.)

The 1880 census for Bridge Creek Township in Ouachita County AR shows this (misspelled) entry:
...Marten L. Michel, 29, farmer, ARK, father GA, mother GA
...Margaret, 29, ARK, father SC, mother ALA
...Thomas T., 4, ARK
...Lewie W., 2, ARK

The HELDEBRAND HERITAGE book doesn't mention a divorce and any info about Martin marrying again. Margaret's parents lived at Bluff City in Nevada County but very near to the Ouachita County line. They had earlier lived in Union County AR too, so there were connections to all three counties, as you can also see from the above info. The divorce was most likely filed in one of these 3 counties, although you also mentioned Old Washington, which is in Hempstead County.