It's funny that you should ask, because it's one of the more gut-twisting parts of all this for me. So I need to take some time here to explain things. We've been married over 30 years, and she started out calling him by his name (Jack) early on, but after a while switched to calling him Dad. She (Kathy) had never been close with her own father, and after he passed away a number of years ago, my dad kind of stepped into a more fatherly relationship with her. It was always "Jack" or "Dad" though, except there were occasional times where the two of them would get into kind of a back-and-forth teasing mood, and she'd say something like, "Would you buy me an ice cream, Daddy?", and he'd say "Can you say please, Katykins?", and she'd come back with a girly "Please, Daddy, Please!". Stuff like that. But it was rare and I didn't think there was anything that weird to it.
On to the present, and how this appears to be playing out now. The first time we all got together after I'd made it clear to him that Kathy might have sex with him, we'd agreed that at first they'd just see if things felt right. Not have sex but just open the door to some physical contact, so that things didn't go too far and we all could then step back and see if everyone was OK with having it go further later. I invited Dad over to watch a football game. We all sat in the den, Kathy and I on the couch but my dad sat off to the side in a chair. The tension was there but no one seemed willing to make a move to take a first step across that big line between father-in-law and sex partner. Finally, Kathy asked my dad if he'd like to come sit next to her. He got up, walked over, and sat down at her side, but not at a normal distance - instead, snuggled right up against her. At that point, I felt my stomach flip a bit. I think the line was crossed right at that point. They sat there for a bit, both appearing to be totally engrossed in the game on TV, but finally she slid her hand onto his thigh, and then started moving it up and down. Again, nothing more for maybe a minute or so, and then Dad put his hand on hers. More delay, until finally she turned toward him and kissed him gently on the neck. He turned to her, she kissed him lightly on the lips, and then it took off from there. Her mouth opened, and the mood changed entirely. It wasn't long before his hand was running over her body and she was breathing hard. In the midst of that, she said something along the lines of, "I probably should call you Jack instead of Dad, huh?", with a little laugh. He said, "No, I'm still Dad." A minute or two later, when they were going at it even more intensely, she said, in kind of a moan, "Can I call you Daddyyy...?" And he replied, "Uh huh. Katykins can call me Daddy if she wants."
They went on like that for a bit longer, and then Kathy abruptly stopped him and said that they really needed to hold to our deal of not going further the first time. All three of us were breathing hard, and I think totally amazed by what had just taken place! They both seemed somewhat embarrassed at how intense they'd gotten, and Kathy said with a laugh that maybe she should stick to calling him Dad.
But now, the two times they've gotten together for sex, they've switched right back into that sorting of teasing, flirty Daddy and Katykins way of talking to each other. She'll say stuff like, "Does Daddy want to kiss me", and then on to things like, "Does Daddy want me to suck his cock?". I can't tell for sure if my Dad's totally comfortable with it, but he's started to play along more, and has said things like, "Katykins has such beautiful breasts" and even the last time finally said in a shaky voice, "Does Katykins want Daddy to fuck her now?" as he mounted her. It gives me butterflies to even relate this. It's crazy, but I find it hugely erotic but also unsettling. It's not a problem, but has definitely ramped up the kinkiness level a lot, at least for me. I asked her later what the Daddy/Katykins thing is about, and she just laughed and said it's all in good fun.