ויבא אל הגר ותהר ותרא כי הרתה ותקל גברתה בעיניה
He consorted with Hagar and she conceived; and when she saw that she had conceived, her mistress was lowered in her esteem.
Sarah had hoped that Hagar and Avraham would have a child together, but she did not anticipate that this would lead Hagar to belittle her. Rashi comments,
אמרה שרי זו אין סתרה כגלויה, מראה עצמה כאלו היא צדקת ואינה צדקת, שלא זכתה להריון כל השנים הללו, ואני נתעברתי מביאה ראשונה
She said, 'This Sarai her conduct in secret is not like her conduct in public. She shows herself as if she is a righteous woman, but she is not a righteous woman, for she did not merit to conceive all these years, whereas I have conceived from the first union.'
Sarah complained to Avraham about Hagar's negative attitude and he told her that she was free to do with her whatever she saw fit. The Torah tells us (16:6)
ותעניה שרי ותברח מפניה
And Sarai dealt harshly with her, so she fled from her.
What exactly did Sarah do to Hagar that caused her to runaway? Rashi writes that she enslaved her harshly. Radak, however, goes into greater detail. He writes,
ומה שעשתה שרי לא היה טוב בעיני הא-ל, כמו שאמר המלאך אל הגר: “כי שמע ה’ אל עניך” והשיב לה ברכה תחת ענויה.
And what Sarai did was not proper in the eyes of God, as the angel said to Hagar: 'for Hashem has heard your suffering' and he gave her a blessing because she had suffered.
Radak claims that Sarah sinned by treating Hagar harshly. He goes on to describe exactly what Sarah did to Hagar,
עשתה עמה יותר מדאי, ועבדה בה בפרך. ואפשר שהייתה מכה אותה ומקללת אותה, ולא הייתה יכולה לסבול וברחה מפניה... אף על פי שאברהם מחל לה על כבודו...היה ראוי לה למשוך את ידה לכבודו ולא לענותה... אין ראוי לאדם לעשות כל יכולתו במה שתחת ידו
She did too much to her and she enslaved her with hard labor. And it is possible that she beat her and cursed her, and she could not withstand it so she fled...even though Avraham gave up his honor...it would have been appropriate for her to hold back for his honor and not afflict her...It is not appropriate for a person to do all that is within their power to a subordinate.
Radak is not alone in his criticism of Sarah. The Ramban criticizes both Avraham and Sarah when he writes,
חטאה אמנו בעינוי הזה, וגם אברהם בהניחו לעשות כן
Our mother committed a great sin with her harsh treatment and Avraham also sinned by allowing her to do this
Rabbi Elchanan Samet (Iyunim L'Parashot HaShavua Vol 1 pp. 33) writes that there is evidence, found in archeological digs that might defend Sarah from her critics. He quotes a Hebrew translation of Hammurabi's Code, the system of laws developed by King Hammurabi who lived during the same time period as Avraham, Yitzchak and Yaakov. Hammurabi's code records the following law,
כי ייקח אישה כוהנת, והיא תיתן לאישה אמה, אם תלד בנים ואחרי כן תשווה עצמה לגברתה, גברתה לא תיתן אותה בכסף, מפני שילדה בנים. היא תשים עליה אות ותמנה אותה בין האמהות. אם לא תלד בנים, תיתן אותה בכסף
When a man marries a woman who is barren and she gives her husband a maidservant, if the maidservant has children and then puts herself on the same level as her mistress, her mistress may not sell her, for she has had children. She shall place a symbol on her and enumerate her amongst the maidservants. If she does not have children she may be sold.
In the time and place of Avraham it was common practice for a barren woman to give over her maidservant to her husband in order for them to have children. However, the maidservant remained a maidservant; she was not on equal footing with her mistress. Hagar viewed herself as being superior to Sarah because she conceived the first time she was with Avraham and she began to act like she was the head of the household. Sarah complained to Avraham and he told her that she was free to do what she wished, because Hagar had acted inappropriately - what she did was against the law. Hammurabi's code called for the mistress to "place a symbol on her", to do something to let the maidservant know her place in the household hierarchy. Accordingly, Sarah and Avraham did not sin when they afflicted her, it was Hagar who sinned by viewing herself as an equal.
Given this archeological evidence, one could argue that Radak and Ramban would take back what they said about Sarah's behavior. On the other hand, perhaps they would stand their ground; such behavior may have been permissible according to the letter of the law, according to Hammurabi's code, but perhaps Avraham and Sarah were expected to not simply abide by the letter of the law, but rather to go beyond it.
Given this archeological evidence, one could argue that Radak and Ramban would take back what they said about Sarah's behavior. On the other hand, perhaps they would stand their ground; such behavior may have been permissible according to the letter of the law, according to Hammurabi's code, but perhaps Avraham and Sarah were expected to not simply abide by the letter of the law, but rather to go beyond it.