Was she in on it with Charles Boyer's character in stealing the jewels? He seemed to use her a lot to get on his wife's nerves, driving her to near insanity. And what was wrong with Nancy? She seemed to have a disdain for Bergman's character and acted like a snot-nosed girl, almost like a teen babysitter. I half expected her character to be chewing gum and saying such short phrases as, "Uh ha" or "Whatever."
She isn't in on it, but hiring her, and the nearly-deaf Elizabeth, was part of his manipulations.
He hires a rather fresh, slutty young woman, who probably wouldn't have gotten a job as the second-in-command of a household staff anywhere else. Then he subtly encourages her disrespectful attitude.
Elizabeth doesn't hear the exchanges that might prompt her to tell Nancy to behave better, so there is nobody there to stop it, or tell anyone that the master is oddly encouraging of the freshness.
Between Nancy's lack of social boundaries and his encouragement, she is indulged in behavior that would have gotten most maids fired in a second.
After she has said or done something inappropriate in Paula's presence, he reverts to the the "I don't know what you are imagining" attitude, or uses her desire to treat the servants as equals for an excuse.
Your description is great -- she was the 19th-century version of the immature type you describe!
Gregory hits on Nancy too and she would have no problem starting an affair with him. In the original play/film "Angel Street" it is made fairly clear that the two are having an affair.
Jessica Rabbit "I'm not bad. I'm just drawn that way."