In "Beggar Maid," is Rose an independent and adaptable woman after her divorce?
I would argue that Rose has always been an adaptable woman. She has altered her behavior often throughout her life, finding a way to fit in to society in any way she can. Her ways of being flexible might be controversial and often involve lies, but she does adapt. Consider her "storytelling" in West Hanratty. Feeling like an outsider, she found a way to become a member of society by being a woman who commented on it and criticized it. It gave her more seniority and a feeling of acceptance.
However, she has never been an independent woman. Her marriage to Patrick is a desire again to be accepted, to have a position in society. This is why the marriage ends in divorce - she doesn't love him. However, this self-realization does not lead her to become independent. She still looks to belong, and becomes involved in more doomed relationships as a result.
Not until Rose returns home to care for Flo does she begin to understand herself. This understanding, not her divorce, will lead to her independence.