The information I have is as follows:
1. On the 1880 US Census for Precinct 1, Ellis, Texas, Roll 1301; Family history Film 1255301; page 379D, Enumeration District 045, it has James H. Taylor, his wife Mary E. Taylor, and their daughter, Josephine Taylor. Also listed was Theodore Simpson, farm hand, born in Illinois. This would correspond with the grandmother, Mary Taylor, on the US census of 1910 in Arkansas, living with David Franklin and Rosa Elizabeth Simpson Alexander.
Josephine Taylor (whose mother was Mary E. Taylor) and Theodore Simpson were married on 12 August 1880 in Ellis County, Texas. per the Texas Select County Marriage Index.
On the 1860 (Year: 1860; Census Place: Township 3 S Range 8 E, White, Illinois; Roll: M653_236; Page: 592; Family History Library Film: 803236) and 1870 censuses, Theodore Simpson was living in White County, Illinois (Year: 1870; Census Place: Burnt Prairie, White, Illinois; Roll: M593_289; Page: 271A; Family History Library Film: 545788).
On the 1870 census, Josephine Taylor was also living with her parents in White County, Illinois. Year: 1870; Census Place: Burnt Prairie, White, Illinois; Roll: M593_289; Page: 272B; Family History Library Film: 545788.
2. Family stories told to one of the great granddaughters, stated that Theodore and Josephine, as well as one of their other children, died of typhoid in 1886. Rosa Elizabeth Simpson was sent to Arkansas to live with her grandparents (James Henry and Mary E. Taylor), who were living in Arkansas at that time. James Henry Taylor, died in 1891, and is buried in Arkansas.
3. I was recently able to get a copy of "Simpson Connections" by Robert H. and Twilah M. (Seefeld) McFarland. On page 41, it states that Theodore William Simpson was born in 1859 near Burnt Prairie, White County, Illinois (which corresponds with the censuses), and married Josephine Taylor in Waxahachie, Texas (Ellis County), and died 26 July 1886 near Burnt Prairie, Illinois, probably of tuberculosis. It states they had two sons, one born 23 May 1881, and the other born in April 1886, and both died in 1886, in White County, Illinois. They had one daughter, Rosa Elizabeth Simpson, born 26 August 1882, Liberty, White County, Illinois.
Also it states "Theodore and Josephine Simpson appear to have resided most of their lives in Illinois except for a brief period when they went with Josephine's parents to Texas where they were married. After the death of her parents, Rosa Simpson lived with her maternal grandparents who went to Dump, Arkansas, where they homesteaded 140 acres. Rosa and her husband, David Franklin Alexander, bought the 140 acres for $15 in January 1900." I would be happy to scan the page upon request.