"They left the village to pursue a group of Indians, and were attacked by Indians from other villages coming to Black Kettle’s rescue." One of the things that annoys me most about many portrayals of Custer is the idea that the Washita was some sort of deliberate cowardly attack by the Army on a known peaceful village. As you just pointed out, there were hostiles in the immediate area; it was just horrible luck for Black Kettle and his band that the trail Custer followed - in the dark - led to that group and not any of the other hostile camps in the area.
Opinions differ on whether Black Kettle was peaceable or not. Most say he was. The tracks of the war party (Custer called it that in his report) the 7th discovered indeed led to his village. Black Kettle may have meant to move his camp closer to the other camps down river, but never got the chance. The site of the battle is near Cheyenne, OK, about 45 miles north of I-40 from the Sayre exit. BTW, the site of the Sand Creek massacre in eastern Colorado, for the most part unconfirmed to history for a century, has been located and
confirmed. There was a recent archaeological dig there by Doug Scott (the archaelogist who first worked the Custer Battlefield). I have Scott's book on the dig. Interesting read...