I'm really sorry about your Dad *hug*
I know I would want to figure this thing out with Molly sooner than later - I would not be OK with somebody saying they wanted to display photos of me but couldn't because their other partner would see them, especially because its about HIS discomfort mainly as far as I can tell, and not necessarily hers - is he going to go through his life never putting up pictures of those he loves because it might be some odd affront to someones sensibilities?
I think getting in touch with her via email would be ideal since for all you know she's fine with things, but his worry about it makes him present the situation as being horribly uncomfortable for her and probably is greatly affecting both you and her the longer it goes on. I've met people Adam dated, and both Brian and Greg's wives without them involved or around, talked through emails or IM to chat and set up coffee or drink dates (sometimes my preference to just meet them solo, sometimes theirs). It's nice not to have a third parties nerves impacting an attempt to get to know somebody, and I have a feeling C might just botch it if you were all in the same place at the same time so... with how much this is weighing on your mind, and how much is going on in your life right now, in your place I'd pretend C wasn't joking and ask him for her email and ask him to let her know that you're going to be writing her.
Happiness will never come to those who fail to appreciate what they already have.