In this episode, both Arthur and Mordred are bound to become enemies even if they don't want. Kara stubbornness leaves no way out. Arthur's offer was very magnanimous; maybe he could have given the girl a time to think, but, in my opinion, he was generous enough. On another hand, Mordred knew that the girl had murdered people and she was eager to do it again. In fact, he was horrified when she killed the guard so coldly. I think Mordred's loyalty to Arthur was not as strong as he claimed. Anyway, Merlin should have freed the girl. She did not deserved it but Merlin knew how much was at stake.
By the way, I am not sure that Mordred got to know about Arthur's last offer to Kara.
Well, now Morgana knows who is Emirys. I suppose Arthur will know very soon. Every single episode of this season I have thought at the beginning "Oh my God! Today is the day!" but Merlin has managed to keep it secret!