As you've discovered, there aren't any really clear markers as to what and who she is referring to. That's part of the charm of the piece, especially to actors, who get to fill in the cracks when creating well-rounded characters out of these fairly short pieces.
Anyways - the clues are that she obviously lost out on something, whether that is a romance or a career move (although that seems less likely because of the time period). Since she talks about New York, it's possible she's referring to Flossie Cabanis, who went to the city and had a relationship with a famous actor. But, if that's what Amelia is referencing, then you can infer that something happened between she and Flossie before she left - perhaps a romantic triangle? If you read Flossie's piece, you'll see that her success and happiness did not last, so Amelia was right that even though she was left behind and died, she won.
Probably, Dora Williams.