Maybe Mordred had stayed on Merlin and Arthur's side if he had known that Arthur gave Kara a chance. Unless Mordred used some kind of superhearing he probably thought that Arthur let her hanged without any chance to stay alive whatsoever, making Arthur kind of ''coldhearted'' to Mordred's eyes. That actually makes a lot difference, in my opinion.
But yes it was quite foolish to follow Kara, but i guess he coudnt abandon childhood friend that easily.
But that's actually the cause of much tragedy, right? The misunderstanding. If only everything was explained, if Merlin could tell his secret, or if he could tell Mordred about his destiny to kill Arthur, if only Morgana was able to practice magic freely, if only Merlin could have spent more time with his father. All these are, of course, thoroughly sad, unnerving and sometimes irritating, but they do produce tragedy. In the end, the point of this show is to tell some story, and if everything worked well, it wouldn't be much of a story, I suppose.