Genna Lannister
Book canon alleges that at some point during the second century after the Conquest a Lannister man mated successfully with a Baratheon maiden. There is a good chance thus that the Lannisters have inherited their propensity for incest through a remote connection with the Targaryens via the Baratheon branch. Therefore, it is not exactly impossible that, before Cersei and Jaime’s shenanigans, a young Tywin might have dreamed to kiss and even more his sister, Genna. This allegation is sustained, in my opinion, by the fact Genna mentions disappointing Tywin at some point. And no, this has nothing to do with Tywin giving Genna the silent treatment for calling Tyrion his son.
Rhaella Targaryen
What is omitted in a text is as important as what is clearly stated.
Under the walls of Duskandale, Tywin has his (first attempt?!?) at promoting 14 years old Rhaegar as an alternative king. While Tywin doesn’t see Barristan coming to save Aerys, there is the historical precedent of young king Jaehaerys and his hand, Rogar Baratheon. While not stated as such, Rogar marries the young’s king mother for two reasons: power of the king through his mother and control over her fertility. Had Barristan not succeed in his attempt to save Aerys, Tywin’s next move after proclaiming Rhaegar king will be to marry his mother. A woman he might be plotting with at this point. Add to this the revenge element of Tywin gettin even for whatever was between Aerys and his wife. And the Lannister lust over silver haired (or not) dragon spawn (see Cersei vs Rhaegar and Jaime vs Brienne case studies).
Olenna Tyrell
Now, far from me to suggest Tywin doesn’t appreciate an intelligent woman… as long as she has the intelligence to play dumb. Outspoken and assertive Olenna Tyrell must therefore be Tywin’s nightmare. A force of nature he cannot stand against. In her way, Olenna Tyrell is the first woman who publicly defied Lord Tywin… since the bitch Ellyn Reyne. From an anthropological point of view, women fear men might kill them while men fear women will laugh of them. Ellyn laughed at Tywin and paid the price. Therefore, give Tywin half a chance and he will deal with Olenna on his way.