Slain was definitely in the wrong here.
Inaho let Slain be his ally because he said "The enemy of my enemy is a temporary Ally". When they established communications, Slain was talkative with Inaho. After the battle, Slain said that the princess was alive and he wants to meet her. As far as Inaho knows, only the rebels who created the original assassin plans know that the Princess is alive, not to mention the fact that Slaine could be a martian from another territory or a double agent sent to kill the princess again. Inaho asked him twice on how does he know that the princess is alive, Slaine went from talkative to being quiet. Inaho gave him multiple chances to answer and Slain assumed that the humans are abusing the princess and trained his guns at him. If you rewatched the episode, you can see that Slaine shot first and Inaho shot back in self defense.
Inaho knew that winning the war would be impossible without getting the princess's help, which he talked to her about in the previous episode. Either way, Slain should have answered Inaho's questions and the situation would be diffused.