As of the start of Clash of Kings, we have no proof that Jaime and Cersei's relationship and its results are known to any but a handful of people. The only living ones being Jaime, Cersei, Tyrion, and (IIRC) Catelyn. (I believe Jaime admitted the truth to Cat at some point during his captivity but I could be misremembering that.) Its likely that Cersei's other lovers strongly suspect the truth -- Lancel is scared witless at what Jaime will do to him -- but I doubt Cersei has actually confirmed those suspicions for any of them.
However, I would speculate that it's very likely that Tywin Lannister knows the truth by that point, for several reasons:
- Stannis told everyone. Stannis's entire motivation for revolt in Clash of Kings is his sincere belief that Joffrey is not Robert's son, and he made sure everyone important knows it. Of course, even people who oppose the Lannisters have written this off as a political tactic, and Tywin certainly rejected Stannis's claim outright, but that doesn't mean he doesn't believe it.
- Tywin is at least as intelligent as Ned Stark and Jon Arryn. If Ned could figure out the truth in a few months at Kings Landing, it seems likely that someone like Tywin would have been able to do so after almost a decade.
- They had been caught before. When they were younger, a servant caught the two of them having sex, causing their mother to separate them. Its not known if she told Tywin about their actions (he would have been away acting as Hand at the time) or not, but its likely he would have suspected something was up in any case.
- Tywin has seen her sometimes-irrational fixation on Jaime in action. Remember, she is the reason Jaime was brought to King's Landing and invested into the Kingsguard, which she orchestrated so she could be closer to him. In response, Tywin quit his post and took her with him back to Casterly Rock, since Cersei just robbed him of his heir.
However, even if Tywin does know Joffrey's true parentage at the point he arrives in Kings Landing, there is no way he would ever speak about it openly, and I find it unlikely that we'll get a POV from him any time soon. So the best we can do is speculate, and my conclusion is basically:
As intelligent and practical as Tywin is, I find it hard to accept that, when confronted directly with the truth (via Stannis), he was unable to come to the correct conclusion.