All the things you mention are what have me so confused. Cindy is such a control freak. Why would she cover up Casey's lies, deny pregnancy, tell George to back off about jobs? And now, lie, when she must know it can be proven. Scattering around like a nervous little sneak. I know it is extremely rare, but maybe Cindy is the abuser??? A control freak would have better control of her daughter. She let ICA run things...WHY? certainly not to protect George. He was told to butt out of everything. And when Lee was testifying, those two siblings were crying agonizing tears IMO. Something happened to them.
ETA: After reading another thread about Geraldo saying he knows the Anthony's thought Lee was the father. Maybe the big secret is sibling incest. They were caught by Cindy, and she put a stop to it, but they grossly thought they were in love. (Heck even Angelina Jolie is suspected of incest with her brother., yuck, I know). This could answer a couple of things.
Lee's promise: I will always love you.
ICA in jail tapes-Don't worry I didn't say anything.
Explains not pursuing who the father is.
Explains ICA hyper-sexuality.
Explains Lee wanting to be at birth-maybe he believed it too.
Cindy lying and covering up so much.-She knows what her kids did and is devastated. Maybe blames herself because she didn't catch it sooner. Explains Lee being odd man out. He as the boy and older would take the most blame. And as control freak extraordinaire, cindy would do all in her power to keep this from coming out. Maybe Baez said, you gotta do this or ICA will tell the truth about the incest. I gotta admit, thats one hell of thing to want to lie about. I would.