Why did Molly mention the story of a 22 year old girl in this scene?

Molly is saying that the girl who got the bag hadn't been raised properly to understand what is important in life.

Essentially, the girl in question prostituted herself (it's implied) just for a Chanel bag!

Charles is teaching Stella the importance of things and ensuring that she will have every advantage in life he can possibly arrange or influence. Primarily this is by being a good parent...something Molly didn't really have.

Molly is indicating her approval of the way Charles is raising Stella and suggesting that he keeps it up.

Molly is referencing common bias (unconscious or otherwise) toward women in their careers and tendency to act dependently on men in their personal lives, tragically losing sight of their own merit / self-worth. Molly is essentially telling Charles to push Stella to achieve all she can, so that she gets what she herself earns by her merit. In the movie, Molly acknowledges her appreciation for her father being hard on her to achieve all that she can.

However, Molly notes that she pushed herself even further on her own, neglecting law school opportunities, because she, unlike her brothers, figured out that her father had not been loyal to her mother. As a result, she pushed herself to wait tables and neglect start from the bottom to sustain herself so that she knew she herself owned all of her accomplishments, not her father / ski coach or anyone else (male or female).

Molly is implying that Stella will benefit from Charles pushing her like Molly's father had pushed her, plus the additional push she'd given herself to ensure that all of her achievement was hers alone...

With this, I reference Molly's quote from John Proctor's character in Arthur Miller's play, "The Crucible," stating that by leaving all names of the dishonest people (mostly men, including Russian and Italian mafia members) in her autobiography, she was protecting her own identity, not any of their names.