Me too. I really, REALLY hope they don't screw up that dynamic somehow. I love that I honestly don't know if Tywin knows she's a Stark or not at this point. He knows she's from a very noble family in the north, he knows she wanted to hide that fact from him, he knows she's on the run and hiding her identity, he knows her father wasn't a stonemason, was educated, and was killed for serving someone, and he's realized she seems to have no problem talking to a lord informally, even gave him a little attitude.....He totally could have connected the dots already.
I wouldn't be surprised if he just straight up tells her he knows who she is in the next episode or two.