I think that what you are talking about here is the time that the Director is saying that he is going to punish Bernard Marx by sending him to an island. He thinks that Bernard is being too unorthodox in his behavior, especially in his sexual behavior.
The Director gets embarrassed (really beyond embarrassed, maybe humiliated is the better word) when Bernard brings John the Savage and his mother Linda into the room.
The fact that the Director has had a child is beyond belief and humiliates him.
I think that the accusation against Lenina refers to a similar accusation -- that she is too sexually involved with Henry Foster instead of being more promiscuous.