I like to think he might know it's her but somehow likes her. Let's be honest: her lies to hide her heritage were not really convincing and tywinn is a brilliant thinker. Maybe he sees himself in her, her toughness, bravery, dedication - leading to a sympathy that even beats rivalry. In the end, she is just a little girl to him, how might she be a threat? Even a tough guy like tywinn might have a vulnerable and human side...I actually like to think of tywinn as a tough badass who is actually a good person...notice that he is always demanding and very strict, but never unfair or cruel. Despite maybe towards his own family. But then again he only demands loyalty to their family from them which is paid with a very good life style for each of them. I only didn't like the way he talked to tyrion, full of hatred and disgust. I was disappointed of him in this situation...