Custer was not the evil man portrayed in films and later write ups. at the Washita he was under orders from Gen Sheridan to attack the tribes who had been raiding in Kansas. His Osage scouts followed their trail through the snow right to the Washita. The Osages were the ones who killed women and children.
https://www.nps.gov/waba/learn/historyculture/osage-scouts.htm
“According to Ben Clark, Custer’s head scout, the blame for the killing and mutilation of Cheyenne women and children at the Battle of the Washita lay squarely upon the Osage scouts because of past atrocities committed against them by the Cheyenne. Custer ordered Clark to stop the killing. The Osage then grabbed tree branches and bushes and beat the fleeing women and children back into the camp.”
The tribe was not on their reservation as it was farther north east in the Cherokee lands, not the Chocktaw Chikasaw lands. They got that area several years later but not in 1868. The bodies of captives Clara Blinn and her son were found near there.
Custer was responsible for the actions of his entire command, not just the white guys wearing blue. If he could not control his scouts, he needed to get rid of them and either get more reliable men or use his own Cavalry as it was designed for scouting.