Why did Tywin destroy Tyrion's marriage?

Question

I've read up to ADWD 2 and maybe this is explained, but if so, I missed it. What was the real reason that ... (spoilers for A Storm of Swords)

... Tywin made Tyrion believe Tysha was a whore, and broke up their marriage. What would this achieve? I know that he's a cold, hard character, but I can't believe that he would be so callous as to force his thirteen year old son to watch as his wife was repeatedly raped before making him have sex with her himself, just to teach Tyrion a lesson. How did it serve Tywin's ends to 1) break up Tyrion's marriage and 2) do it in such a sadistic way?

Answers from the books or the series are acceptable.

Answer 1

I think there are two primary reasons for both breaking it up and for being cruel about it. First, he wants to ensure that Tyrion doesn't attempt this kind of marriage again since the Lannisters can't marry commoners as they are nobles, Tyrion could potentially be useful for a political marriage, that sort of thing. Being brutal will make sure it doesn't happen again. Also, he wanted it to appear that Tysha was a whore rather than an honest girl to ensure that Tyrion did not trust other women.

Second, Tywin hates Tyrion for multiple reasons. First he has to put up with the shame of having a dwarf for a son. Second, it has been hinted that he is suspicious that he may not be Tyrion's actual father (because Aerys Targaryen was interested in Tyrions mother, Tyrion has non-typical features for a Lannister, genetic deformities run in the Targaryen line due to inbreeding) . Third he blames Tyrion for his mothers death.

In the end this was not some brilliant political play, in fact it was probably relatively dangerous for Tywin as opposed to some simplistic revenge like straight up having her killed. We can only explain this by saying that the end purpose was to hurt Tyrion.