I have characters that are in a small expedition (sort of like the Terra Nova expedition but on a much lesser scale), and most of them, including the 2nd in command, want to plan a mutiny against the Captain. The story takes place ~1915, what were policies around mutinies then?
Mutiny was generally punishable by death by firing squad or hanging. Point of note if the officers including the second in command feel that the commander is unfit there is provision for them to remove him from command without it being mutiny, but they 'd be taking big risk, because if a court martial didn't agree with them they could still be considered mutineers.
That’s not long after keelhauling has been outlawed in the west, so depending on your story, you could get away with it. That said, flogging was the go-to punishment. It was a very effective and efficient punishment. Only deadly when that was the intention, but still painful, quick and easy to organise, and great for a show of terror. Also, doesn’t permanently maim, which is very important on a ship. Like the poster above said, the punishment for mutiny was death, but you can’t always just kill off half your crew. So the leader ring would get the rope, whether that meant hanging or drowning, or a bullet. The rest would get the whip.
flogging round the fleet was common in the british navy for mutineers who were ring leaders - ie 20 strokes from every ship in port... flogging to death in essence although a few hardy souls survived it.