Really, that's not all that important if it means sacrificing Tyrion's and Tywin's character as a whole to do it. Tyrion being the Mad King's son is not enticing or interesting. All it does is turn Tywin into the Evil Stepfather, gives Tywin motive for hating Tyrion, and lets Tyrion completely off for murdering his own father. That's not interesting. It makes the relationship between the two characters much simpler, and simultaneously makes less sense.

If Tywin even suspected that Tyrion was Aerys child of rape, he would have had a servant through him off a cliff face from Casterly Rock and resigned from being Hand much sooner. I also think he would have almost immediately joined Robert in Robert's Rebellion (although Jaime makes this one a bit more iffy than the other 2).

Tywin's hatred for Tyrion is interesting because Tyrion is a twisted form of Tywin. He shares all the same attributes as his son, from his calculating nature, to his shrewdness, to his intelligence, his gift for governing, to his shaky relationship with his own father, to their mutual love of whoring.

The only thing that really separates the two of them is how they were raised. If Tyrion was born in Tywin's body, he would have turned out much the same, and vice versa. Tywin became joyless because of his father, while Tyrion took laughter up as armor, which of course pisses Tywin off even more. This is what is interesting, in how a father treats his own son so horribly and has his own son's wife gang rapped in front of him only to have his son finish him off.

Now, let's take it from their POV's if they were to find out about Tyrion being Aerys son. For Tyrion, he'd laugh, tell his evil stepfather's memory to frick off, and then laugh again when he considers how Jaime will react to this bit of news. He will not give a frick if he's Aerys son, just so long as he's not Tywin's. As for Tywin, he'd feel validated for treating his son like complete shite and then command Ser Meryn to kill him in his sleep. I instead find it better that Tyrion killed him for being a cesspool of a father instead of just an evil man who tortured him.