Of course, we could also argue that the "American wife" is ready to be something other than the American girl we see her as. She's restless. She has nothing to do with herself. The way she springs into action when she sees the cat tells us a lot about just how bored she is. The idea of rescuing a cat offers her a temporary sense of purpose, and perhaps even a more permanent purpose if she gets to keep it…never mind the fact that she's far from home in an Italian hotel.
Think, too, of the list of "wants" she spouts when she returns to the room: a cat, her own silver, candles, her own dining table. She doesn't explicitly say she wants a home, but that's sort of where all of these things belong, right? The other things she wants, long hair (when she has short hair), springtime (when it's not), and new clothes are all desires for change.
You might think she sounds like Veruca Salt from Charlie and the Chocolate Factory—the little girl who wanted everything and wanted it now—but the American wife isn't quite in the same category of spoiled-rottenness, though she is filled with desire for something other than her present circumstances. She and her husband are living a kind of suspended, floating life—reflected in the fact that they're living in a hotel room. Juxtapose this, as Hemingway does, with the hotel owner, the padrone, and what he represents to the wife: something solid, old, respectful, dignified, serious. All of these attributes belong to the kind of dream-life she imagines as she sits in front of the mirror. You might say that it's her very American-ness that she's sick of—it's what she wants to trade in for the old, solid values of an older and more established country, like Italy.
Still, on the other hand (If you don't have a third hand, borrow one from a friend for a sec), the very rashness of wanting all these things that can't be and that her present life and marriage can't give her, seems to be part of the same impulsive, untethered American spirit that the wife wants to get away from.