Iori has almost zero right to be pissed.
She doesn't have the right to be pissed about Seto being with another girl, she slapped him and then ignored/avoided him for a couple months.
She didn't bother to listen to anything he had to say after Izumi showed up at the inn, or question him about anything. She's done a pretty good impression of not liking him.
She butted her nose into the business of a girl who's practically a stranger, regarding what she was doing in the bath. Admittedly, she went along with her friend on it, but it amounts to the same thing.
And while Izumi asked the wrong thing, her telling him off after he was discovered in the bath didn't leave him any room to say anything, and made it clear she didn't want an explanation.
The only thing she can legitimately be upset about is that Seto was in the female bath with a girl, and she didn't think he would do that.
At least Izumi is turning out to be pretty down to earth and kind, and not as crazy as it looked before. It probably won't be a Seto x Izumi ending... but that's what I favor right now.