Hi Leonard,
I would say your statement "The role of the Native American in the CW is complex" is the understatement of the day! ;-) Both of the Cherokee factions allied with the Confederacy or with the Union had a primary interest -- keeping their soveriegnty and landbase as a nation. The US Supreme Court coined the designation "domestic dependent nation" to the Cherokee which was applied to all the so-called Five Civilized Tribes (Cherokee, Chickasaw, Choctaw, Muscogee or Creek, and Seminole). They did not want to be US citizens -- I only mentioned they were not US citizens to say there were three regular Union regiments made up of non-US citizens (except for white officers). They had their own governments and systems of law and national boundaries. They had decades of treaties with the US and were dependent on the US govt in many ways. The more traditionalist factions of the tribes wanted to remain neutral, an impossibility, but had close ties to their anti-slavery missionaries and looked to the US for protection. The more progressive, capitalist, rising middle-class, businessmen factions of the tribes had economic ties to the adjacent southern states, understood US politics better, were English-educated and sent their kids to schools in the adjacent states.

I didn't mean to overstate the connection between Watie's 1st Cherokee Mtd Volunteers and Quantrill, Livingston, and others. The records do show a few of Watie's men on detached service with Livingston -- probably Missouri men in Watie's regiment. The Cherokee did have business ties to southwest Missouri and northwest Arkansas. Folklore says Quantrill was staying with a Cherokee and accompanied an "unofficial" contingent of Cherokee to Wilson's Creek in 1861. Col. Adair, of the 2nd Cherokee Mtd Vols, mentions in a report in 1864 that he heard Quantrill was passing through the vicinity (in the southwestern Muscogee Nation) and that he hoped to connect with Gordon for a raid into the Cherokee Nation. When Watie was encamped near Webbers Falls in the Cherokee Nation (1862-63), Livingston had a picket and a smallpox hospital just a few miles down river watching the right flank.

I'm not familiar with Alvin Josephy's book. I would recommend Edward's "The Prairie was on Fire: Eyewitness Accounts of the Civil War in the Indian Territory" and the chapter on the Indian Territory in Mark Christ's "Civil War Arkansas 1863: The Battle for a State".