In contrast, Young couldn't be successfully prosecuted for stranding Rush. He can't be forced to testify against himself, and there were no other witnesses since Rush was unconscious. Rush could try and make something up, which is just he said/she said, and Rush's testimony would already be compromised because of his actions regarding the gun, which shows he is perfectly willing to lie and frame Colonel Young. So his testimony would be disregarded.
So really, nobody could make a successful case against Colonel Young, except perhaps a military court that might find he acted without good order and discipline. You could certainly charge Colonel Young with assault and battery, but again, you can't prove who threw the first punch unless Colonel Young is willing to testify against himself, and Rush's testimony can't be trusted because he'd already tried to frame Colonel Rush for murder. On top of that there's a clear case against Dr. Rush for hijacking and mutiny.
So we're just left with rumors and discontent about Young amongst the civilians, but nothing that would provide a legal basis for removing him from command except a judgement by his military superiors that he has an inability to lead.