In what ways are Lilly's interactions with Rosaleen similar to a girl's interactions with her mother in The Secret Life of Bees?I just don't understand the question.
The relationship between Lily and Rosaleen does have some mother-daughter aspects. Remember that Lily is motherless, and Rosaleen is the adult female in the household. She takes care of Lily, cooking the meals and maintaining the house. She gives Lily love, rescuing Lily from her father's extreme punishments and celebrating her birthday. She sets limits for Lily, just as a mother would do.
What might be confusing about the question is that there are aspects of the relationship that are not like those of a mother and daughter. For example, because of race relations in the South in the 1960s, Rosaleen is considered "unequal" to Lily because she is African-American. This gives Lily the ability to act in ways that she could never act with a mother, such as persuading Rosaleen to run away. Also, there are ways in which Rosaleen is really looking for a mother figure for herself, too, which makes Lily and Rosaleen more equal, with both of them really searching for mothers.
It might be interesting to write a compare and contrast paper on this topic. Can you think of other examples of how Rosaleen is like Lily's mother? Can you think of other reasons she is not like a mother to her?