Honor of House Lannister

For all Tywin’s talk of Tyrion bringing dishonor on his house and trying to restore it after Tytos, couldn’t it be argued that Tywin’s actions (along with help from his children) bring more dishonor on his house than his father did?  

The honor of his house has become a joke with people saying Lannisters have shit for honor and Kem’s “Lannisters are twisty snakes.”