Elizabeth is a self-obessed high-society type. She claims she's never wrong about anything and only cares about how she looks. Despite this, she has a wild side that she eventually lets out by the end of the film.
When Frederick was called to Transylvania to take care of his late grandfather's estate, the two had a comically awkward goodbye, due to the fact that Elizabeth's hair, dress and makeup were at risk of being messed up if they were too passionate.
By the time Elizabeth arrives in Transylvania, Frederick has fallen in love with his assistant Inga. The two have a moment together before the creature kidnaps Elizabeth, but whatever romance they used to have has since passed by this point. Frederick didn't even notice she was missing.
By the end of the film Frederick and Elizabeth have called off their engagement and have married other people.
Elizabeth appears in Transylvania sometime after Frederick has created a new creature. The creature kidnaps Elizabeth and forces himself on her. Due to the creature's oversized genitalia and enhanced stamina they have sex several times. Elizabeth enjoys every moment of it and forgets all about Frederick. By the end of the film they are married, with Elizabeth now styling her hair to look like the creature's bride.
Ina was Frederick's lab assistant in Transylvania. Due to her beauty Elizabeth was immediately suspicious of her. Of course she had every right to be as Inga and Frderick had just had sex moments beofre she arrived. Whatever rivalry might have been between the two women is soon forgotten as Elizabeth and Frederick call off their engagement.