While there is a woman named Tansy in the text—the proprietress of the Peach (III: 330, 331)—it seems very unlikely that she was the person Lord Hoster was referring too. For one thing, his cries were rather anguished, and for another is that a revelation that he slept with her seems to have no bearing to speak of on the story (the one possibility is that she had a child by him, a bastard who might stand as heir—but it would be strange for this to never have been brought up.)
Far likelier is Catelyn’s interpretation (III: 31) that Lord Hoster was recalling the time when Lysa was unwittingly given an abortificant, in large part using tansy (III: 913), to get rid of a child she was carrying. This child was Littlefinger’s, as Lysa indicated that. It should be noted that some think that Lysa’s recollection and claims cannot be trusted at all, given her hysteria and inability to separate fact from fancy (see her sincere beliefs that the Lannisters wanted to do harm to her and her son, based on her lies that they were behind Jon Arryn’s murder).