you have some rewatching to do
http://youtu.be/ihIaJnqxNYc
Tywin was Hand of the King to King Areys II (the "Mad King"). If Tywin didn't directly betray the king back then, and didn't just find one of many ways to get rid of Tyrion, what on earth makes you think he'd be in a scheme to assassinate his grandson?
Joffrey might have been an evil little shit who caused a good deal of trouble, but he definitely wasn't as bad as Areys Targaryen; killing him would leave Tywin with only one really good trump card - Tommen. And even though Tommen is shaping up to be a much better candidate than Joffrey, its not an ideal situation when kings are dropping like flies...