The Chassidic Dimension - Chayei Sarah

Does this means that it was Sarah influence that changed Hagar's personality and behavior? That although during the time when Hagar married Abraham, and Hagar became proud and disrespectful towards Sarah, Sarah was able to show Hagar the true characteristics of a real Royal Princess in the spiritual sense?
Then it shows very clearly that by Hagar marrying Abraham the second time, and her changing her name, it did not mean that her spiritual status was changed. It was only her personality that was changed. And conerning the relationship of servant/slave, this is so very true. The way I see it, a servant/child love his Master/Father. And all desires is to please the beloved.