Hi Michael,
I think it's a totality of the circumstances that leads to Dr. Friskin making the intuitive leap - Clark and Superman leave at the same time and return at the same time (which can be explained by the cover story). Clark and Superman both getting secretly married the day before they left is a tougher coincidence to accept. In Dr. Friskin's case, it is this particular piece of evidence that causes her to realize that Superman is Clark Kent.
In the background, there are other things at work. Dr. Friskin has already figured out Superman is married to Ultrawoman. Couple that with the timing of Lois's pregnancy and Ultrawoman's six month disappearance (yeah, I know, I'm asking people to remember way back when), and I think her intuitive leap makes sense. I'm also banking on the fact that Dr. Friskin has been shrink to both Lois and Ultrawoman, so the similarities there should also be a clue. And she knew that Lois was close to both Clark and Superman. Finally, in all of his retelling of what happened on New Krypton, Superman never mentioned Clark.
As to why Clark knew that she knew, I think for him, the secret wedding was evidence enough to give him away. In his previous sessions, he has also thought that he wasn't doing a good enough job of projecting the air of Superman, so he thought he'd given himself away. If Dr. Friskin hadn't already figured it out, I think he would have spilled his guts at that moment.
I would love to know if you, dear readers, think this needs to be spelled out more in that scene, or if Dr. Friskin's snap deduction makes sufficient sense.
