I did not understand clearly why was Shae having sex with Tywin, I know it is not directly said that they actually "shared bed", but the description of the death scenario speaks by itself. I mean, seriously, why would Tywin Lannister do it with his Dwarf son's dirty whore? I understand Cersei's surprise when discovering Shae's body. I would believe it either. Was it a way of insulting his son? Or he was just enjoying her since tyrion brought her to his tent? Or where they not actually in bed and it was Tyrion's way of humiliating his father?