I've not read the books, the below is just my speculation in relation to the above point.
I think Stannis knows what she did because each time Davos wanted to discuss what he saw, Stannis didn't want to talk about it at all. Also, I think I recall him saying that they have to use the red-witch as you don't win wars with conventional methods (this was before the monster thing appeared). Also, he was present when the old guy died after taking the drink that was poisoned but she was completely unharmed so he must know there is something completely weird about her.
As I said before, I think Stannis left her behind because he was confident he good take King's Landing by himself and the army he obtained from Renly's death. He didn't expect Renly's lover to align with the Lannister's and for them to go to King's Landing to rescue cnut Joffrey.
Speculation is meant to spoilered according to the forum rules isn't it, but then we are talking about a past episode so I'm not clear on that. Anyway
Yeah he must know there is something weird about her, he left her behind, he saw her drink the poison, he made Davos take her to shore.
But it is weird, did he think she was pregnant? She promised him a son.
But it is weird, did he think she was pregnant? She promised him a son.