I do not believe that Tywin knew about that Cersei’s children were not Robert’s. So if you think this as well how do you think he would have reacted if he had found this about before the beginning of the series (say when he was in King’s Landing for the tourney just before Jon Arryn was murdered). And is there something he could or should have have done at this point?

It’s an interesting question. It’s not clear whether Tywin would have believed most sources, given his obsession with Lannister legacy and reputation. 

But to an extent, he’s caught in a fait accompli. He can’t change what Cersei and Jaime have done, nor is he about to condemn them and lose everything. Short of somehow arranging the death of Joffrey and Tommen, forcing Cersei at gunpoint to bear Robert’s son, there’s not a lot to do.

The main thing that would change is his attitude to his kin once he arrives in King’s Landing after Blackwater. He’s not going to listen to a damn thing that Cersei has to say, so he might not be as down on Tyrion. He might rethink his plans re Jaime as Lord of Casterly Rock, but he’d probably look to any of the rest of the family before Tyrion.