I think he absolutely knew about the incest and was going to use that to set aside those kids.
Really? It seemed to me that Renly was genuinely surprised when Catelyn corroborated Stannis’ story, before deciding that it didn’t really change anything.
Plus, Cersei seems to think that Robert means to set her aside and Robert has no clue about the incest.
I’m pretty convinced about this. No way does Mace Tyrell let his daughter be turned into a royal concubine, or let some other woman’s kids come before his grandkids in the line of succession – Renly had to tell him something to convince him. In ACOK, Renly doesn’t want to admit that it’s the truth, because that means Stannis is the rightful heir – and given how Catelyn’s responding, it potentially means the Starks side with Stannis. As long as Renly pretends that Joffrey is the legitimate king and might makes right, he’s no less or more a rebel than his brother in the eyes of his bannermen and Stannis’ claims are mere self-interested propaganda.
She thinks he will, but in association with Renly’s plot. And Cersei knows her secret’s out – JA knew, Stannis probably knows, etc.