Even before Joffrey’s murder, do you think Tywin was looking for a way to rid of Tyrion? Cersei’s accusation gave him pretext, but it seems to me that if he wanted to keep Tyrion around, it wouldn’t have been that hard for him to say something like “the Queen is sick with grief,” asked the nearest Kingsguard to escort her to her chambers, and shipped her back Casterly Rock as soon as possible when she made her accusation.