I think your mother then would have been 3/4ths Cherokee and that would make you 3/8ths. Given there was no Cherokee on your father's side. I had one full blooded Cherokee great grandmother. I've seen the pictures. I've heard it said that so many people have Cherokee ancestry because they were attractive people and the old timers often took them as wives above any other tribes. I think one could be purchased for a horse or two or a good rifle.
3/8th's! Is that enough to get preferential treatment? :) I've not seen pictures of them when young but my mom was quite pretty, definite Indian nose.