If Lady Chiltern is the good angel of feminine modernity, Mrs. Cheveley is the dark angel. She's as Machiavellian and power-hungry as they come. Independence is her god. She may have to be married for economic reasons, but she won't conform to the role of a traditional wife. "Romance should never begin with sentiment," she says, "It should begin with science and end with a settlement" (3.101). In her mind, the best are those mutually back-scratching arrangements, such as she had with Baron Arnheim. She provided him with sex, he provided her with money. She's hoping for something equally streamlined and mutually beneficial with Lord Goring.
On the surface, Mrs. Cheveley is Lord Goring's match in wit, style, and unconventionality. They are both self-absorbed dandies who circumvent social expectations to gain freedom. They don't care what people say about them. We can imagine how they would have ended up together, as younger folks who knew themselves less well.
The problem is: at heart Lord Goring's romantic, while Mrs. Cheveley's pragmatic. Her pragmatism has to do with circumstance: "At that time I was poor; you were rich, " she tells Lord Goring of their engagement (3.221). Who does this sound like? Remember this: "I was twenty-two at the time, and I had the double misfortune of being well-born and poor, two unforgivable things nowadays" (2.21). That's right – Sir Robert and Mrs. Cheveley are two peas in a pod. She was poor and ambitious, just like him. Mrs. Cheveley may be the play's villain, but by giving some hints at a motive we can understand, Wilde helps us see her as a human being.