The North Carolina Cherokee are the ones that didn’t agree to travel The Trail Of Tears to Oklahoma. The Oklahoma Cherokee are the ones that went along to get along. They are two different Cherokee governments. What one does has no effect on what the other does.
The Cherokee Nation should have their own state, as was promised by the Confederate States of America. The CSA granted the Cherokee citizenship in the CSA (something the USA would not do till 1920). They even had representation in the CSA Congress in Richmond. But the south lost the war and the victorious Federals took a sweet revenge upon the Rebel Native Americans. The highest rank issued to Black Federal troops was Master Sargent. The Highest rank given to Native Americans in the Confederate army was Brigadier General.
The North Carolina Cherokee definitely were removed to Oklahoma, although a number hid in the mountains and refused to go
There is even a long running outdoor drama called Unto These Hills that relays the storyline of the removal
The present day North Carolina Cherokee are proud of their heritage and govern themselves well