The Black Hills do run into MT from SD. Not picking a fight...it’s just geography...The Black Hills National Forest is located in southwestern South Dakota and northeastern Wyoming. You are correct, that the battle happened near the Little Bighorn River near Crow Agency, Montana.
The expulsion of the Sioux from the Black Hills is a sad parallel with that of the Cherokee from the Great Smokies. In both cases, gold seems to have been the motive.