I don't buy the daughter theory...
...The theory in which Bill and Alice leave their child with those guys at the mall. It doesn't pass the smell test to me.
For one, if you're going to give your kid away to strangers, I'd imagine you wouldn't do it at the most public place possible, a mall in the 90's at Christmas-time! All the kid has to do is start kicking and screaming and a huge scene would be created. You'd do this in an empty parking lot, not in a place packed full of potential witnesses and hero's. Secondly, while shopping, Alice cringed when she looked at a price tag on an item the kid wanted. Like you'd care what the price is of something you have no intention of buying. Lastly, people point to the "We have to do one thing immediately...F" line as some sort of clue that they're going to replace the child with a new one. Sorry but your mind is going to be on "How in the F do we explain a missing daughter to the local authorities, assuredly soon the FBI, and our families?!" rather than sex at that point. Alice was obviously referring to the fact that Bill was out trying to get laid and she was fantasizing about other men as a reason why they needed to F to get their marriage back on track, get back to normal. Simply getting pregnant and having a new kid doesn't hide the fact that you already had a kid and it's missing! Coming from a rich NY doctor's family, the FBI would assuredly get involved in the case. It would be risky on the Illuminati's part as well, knowing the FBI will soon be putting pressure on someone who knows the location of two of their home residences and the identity of at least one member of their group.
Also, I've known a lot of women in my days...if I were married to one of them and my actions led to us having to give our only child away to gangsters, I'm quite sure her reaction, immediately upon giving away the child, wouldn't be "Ok, let's go home and screw, get me pregnant!"
I don't buy it.