In 21:10 Sarah is demanding Avraham send away Hagar and Yishmael. She says, "גרש האמה הזאת.." -banish this maidservant....
Why does Sarah call her "this maidservant" rather than calling her by her name and saying "banish Hagar"?
Sarah knew this is what needed to be done. It was dangerous for them to continue living in the house with Avraham, Sarah and Yitzhak. It was dangerous for the spiritual growth of the family and dangerous for the development of Yitzhak. She knew she had to banish them.
Sarah also knew that it would be very difficult for Avraham to do so. Avraham was the epitome of hessed. For him to banish them into the dessert would go against his grain. Not only that, but Hagar was a daughter of a king. She was his wife. She was the mother of his child. His child would be banished as well. This would indeed be very difficult for Avraham, even if he knew it had to be done.
Sarah used what we call in psychology "dissociation" in order to make it easier for Avraham to process and accomplish.
By calling her "maidservant" instead of Hagar, Avraham would be able to compartmentalize and think of it as if he is banishing his maidservant, which is much easier than banishing his wife Hagar.
When facing a difficult task, one can take lesson from Sarah and use dissociation in order to better accomplish it.