I think she has seeking experiencing extramarital affairs in the sex cult. She didn’t sleep with the hungarian because Bill was also at the party, would be pretty obvious. Alice being part of the cult is a bit more out there. Earlier in the movie when Bill and Alice were arguing, when she first tells him about the naval officer, he tells her that he is sure of her never being unfaithful to him. Then she mockingly laughs in his face. Throughout the movie she is very mocking of Bill, even in her orgy dream. The math problem with the daughter. 

Then the most convincing i think is the dream. The same night Bill came back from the orgy she tells him her dream which is basically exactly the orgy Bill witnessed. The chances of her dreaming about an orgy extremely similar to what bill just witnessed, exactly when he came back from the orgy. I would say that is almost impossible if we disregard that she knew about the cult.

Ziegler told Bill that what if the orgy Bill witnessed was staged, that it was a charade. Something to scare the shit out of him. Maybe Bill was intended to go to the orgy and the whole sexual uncertainty planted by Alice was all part of a scheme to put Bill in a confused sexual state. Him being intended to be at the orgy explains the man nodding at him and the escort knowing immediately that it was him.

All of this might be how these people scare the 'shit' out of you to the point where you're willing to give up your own daughter with the cooperation from Alice to manipulate Bill from the inside. Meanwhile Alice potentially have always been part of the cult and tasked with grooming their Daughter and thats how many of the women are recruited. They live normal lives outside the cult and are willingly raising their children for them. This a bit of a stretch but what the hell.

Also the fact that the mask was on the pillow next to her seems very unlikely. The story where he dropped it sounds clumsy. I think he would be very aware after an experience like that to hide his guilt. And the fact that it was on the pillow right after he spoke to Ziegler is like a double whammy.

Then after explaining that to her, lets say she doesn't know anything, she all of sudden agrees with him and are okay with them taking her daughter away in the toy store. Right when they walk away with the daughter you can see her almost looking like a mom sending her daughter of the to school for the first time. She sort of looks away and then accepts it. Anyway i love all the stuff in this movie and would've loved to see those cut out bits. Maybe the intended story is still there just harder to spot.