We have a thread going about Custer being victorious at the Little Big Horn. Here's another one.
Before I get into that, let me digress a moment. Onr of the problems that the 7th Cav. had was that they were armed mainly with Springfields. [single shot breechloaders, which tended to have problems with black powder fouling the barrels.] I've never understood why, 11 years after the civil war, the War Dept. hadn't given everybody repeaters. There was the Henry, Winchester, Spencer, to name a few. The troopers had revolvers, but they needed repeating rifles.
OK, so in this TL, Custer doesn't disobey orders, and waits for Genl. Terry, and Col. Gibbon to arrive, and they launch a coordinated attack with artillery, and overwhelming superiority in numbers. I don't know what plan Terry might have used, but I imagine they would have won the fight fairly easily, even with the Springfields.
To sit back and shell the Sioux village would have been a slaughter, I'm actually glad this didn't happen.