Who Mrs Walker is
Mrs Walker belongs to the American community in Rome that watches Daisy Miller's conduct closely. She is well meaning, but she judges Daisy through the rules of her social circle.
Her concern becomes visible when she sees Daisy walking on the Pincian Hill with Mr Giovanelli. She asks Daisy to enter her carriage and leave her Italian companion behind.
What Mrs Walker wants
Mrs Walker wants to guide Daisy away from behaviour that the American community considers improper. She sees the carriage as a way to rescue Daisy from an outing that invites gossip.
Daisy refuses to get in, seeing no reason to give up her freedom. Their disagreement reveals the distance between Daisy's confidence in her honesty and Mrs Walker's concern about appearances.
Mrs Walker and the others in the story
When Daisy attends a party at Mrs Walker's house, Mrs Walker turns her back on her. Daisy feels the hurt, though she covers it with a laugh.
Frederick Winterbourne stands between the two women during the disagreement over the carriage. His uncertainty about Daisy leaves him unable to offer the clear support she might need.
Questions
Who is Mrs Walker in Daisy Miller?
Mrs Walker is an American living in Rome who tries to regulate Daisy's social behaviour.
Why does Mrs Walker offer Daisy her carriage?
She wants Daisy to stop walking with Mr Giovanelli because the outing attracts social disapproval.
Is Mrs Walker kind to Daisy?
She means to help at first, but later treats Daisy coldly for refusing her advice. Her concern shows how easily guidance can become punishment.