I can answer your question about the Who and the Where of William Hammond Garrett, but I believe some of the story about his service and family has been confused. Wm H. Garrett born bet 1819 and 1821 [based on census records] S.C. was the Creek Agent beginning in 1853. Many published records confirm his service as their agent. On the 1860 Census, Wm H., his wife Mary Dickerson Logan Garrett is living with him along with his 2 year old son Wm H. Garrett [Jr] born 1858 Indian territory as their Creek Agent. Also on this census record is John Thornberry the Creek 'Teacher', his wife and a few places later, is dau Sarah C. Skidman living with another woman. William H. and Mary married in 1857 Indian territory, her father was also a Creek Agent, Col. James Logan of Arkansas. Her brother David P. Logan was a trader in the Creek Nation. Her brother in law William Whitfield was also a trader there, and her younger sister Amanda married in the Creek Nation at the home of her sister Nancy Whitfield. As for the story about a child named Elizabeth "Lizzie", You may have connected to the wrong family. William Hammond Garrett did not leave IT. His wife Mary is said to have gone home in 1859 when her father Col. James died. The couple are in AR courts for the initial settlement of his estate - so he was in AR with his family in the 1860's. On the 1900 census, Mary indicates that she had two children with only one still living. Her son Wm H. Garrett Jr is living with her, her dau Mary died in 1870 and is buried with her mother and brother in the Fairview Cemetery, Van Buren, Crawford Co. AR. William H's dau Mary was born in 1863 according to her beautiful headstone. Her exact DOB can be calculated as her stone reads 7 years XX months and XX days, however, the month and day are pretty well worn so I won't offer a guess for them. Garrett's story in the publications Oklahoma Chronicles is correct about his service. His brother John H Garret is living with him on the 1860 census. By 1870, Mary, Wm Jr and her nephew William Whitfield are living in Arkansas. By 1880, William Jr is living with his uncle Jonathan Logan and his family in Yell Co. AR. John H, brother of William, is also living in Yell County. At some point, John H left AR and is found in the Garrett cemetery in Cherokee Co. AL. He is buried along with his mother Mary and others of that family. William H. Sr did serve in the War Between the States on the Confederate side and died, never returning home. Mary was a widow as shown on the census. She died in 1914 and is buried in Arkansas with her headstone inscribed by her surviving nieces and nephews whom she raised after the death of their parents. Her son Wm H. Jr never married and was the sheriff [policeman] of Van Buren until his death.
I hope this helps your search and you may find more information on your g grandmother Lizzie from the Skidman genealogy for children born or raised by them.