Now what if there’s a reason for Tywin being so hard? What if the Lannister brats are not his children, not just Tywin but the whole brood? In the series we’re told how the mad king had a crush on Tywin’s wife. During their wedding and bedding ceremony it’s said that he took liberties with her that normal people don’t take during a bedding ceremony. This could have gone much farther than was mentioned and much longer who’s to say he didn’t father some bastards of his own?
It also isn’t shown in the series but in the books Tyrion Lannister’s hair is a mixture of black and some shade of blonde approaching Targaryen in the color spectrum. His eyes also possess the unique quality of being different in color one black and one green. Tyrion Lannister could be a Targaryen which could explain the reason his father said this when Tyrion asked for Casterly Rock. Resenting someone who calls you father because the love of your life died giving birth to him doesn’t make sense. If anything it would be more reason to love Tyrion, a memento for Tywin before Joanna Lannister left this world. Jaime and Cersei? A Targaryen origin would explain their inability to stay away from one another, not to mention Jaime lacks his father’s craftiness. Jaime is a soldier, one of the best there is politics, accounts and deception are not his forte. Being cuckolded so frequently would explain why Tywin is such a bitter man, knowing that what he raises is not his own, having worked so hard to be better than his father who almost led the family to ruin. His heart is hard but only because it was hardened. To the outside world Lord Tywin might be one of the most feared and respected men in the realm but privately he knows that his success can only be measured in economic terms because he falls short when a social ruler is used.