I agree with shinta, any change in her behavior became clear minutes later that she was just barely holding it together hiding her health issues. She doesn't want Kiritsugu to find out not only because she doesn't want him to worry, but also because she doesn't want him to lose his composure in public.
I'm convinced that while she is more sympathetic to Saber's disdain for Kiritsugu's methods, she's not in any way opposed to how he is doing things. The Einzberns are not good-hearted magi. They harbor no illusions about how the wars are fought, since they are one of the original families. Even her daughter, Ilya, is one of the most pragmatic and cruel magus in FSN, and look how happy and innocent she had been raised by her parents. She was never opposed to using less straightforward means, in addition to just having Berserker smash everything.
Iri does not share the pure-hearted naiveté hidden by bluster that Rin does, the knightly stupidity that Shirou does, or the righteousness that Archibald did and even Kariya seems to have in his own level of sacrifice. She's kind, but incredibly stern when she needs to be. In episode 8, she was asking that Maiya shoot Kirei in the back while she held him in place, before they found out how much of a monster he was first hand.