Genesis 16:6

And Abram said to Sara, Behold, thy handmaid is under thy authority: do to her what is right in thine eyes. And Sara afflicted her, and she escaped from before her.

AND SARAI DEALT HARSHLY WITH HER, AND SHE FLED FROM BEFORE HER FACE. Our mother did transgress by this affliction, and Abraham also by his permitting her to do so. And so, G-d heard her [Hagar’s] affliction and gave her a son who would be a wild-ass of a man, to afflict the seed of Abraham and Sarah with all kinds of affliction.

שפחתך בידך, for she has not been given her freedom by you who are her mistress.

ותענה שרי, Sarai's objective in maltreating Hagar was to remind her of the fact that she remained her slave. She was not to insult her mistress any more. She meant to make clear that any gentile who insults Israelites will experience similar harsh treatment. Compare Isaiah 60,14 והשתחוו על כפות רגליך כל מנאציך, "all those who reviled you shall prostrate themselves at your (Israel) feet."

ויאמר ... שפחתך בידך, Avram meant that in spite of Hagar sleeping with him, i.e. being accorded wifely privileges from his side, she remained Sarai's slave and as such Sarai could determine how to treat her. He made it clear that his own dignity was not to be a consideration in Sarai's treatment of Hagar.

ותענה שרי, Sarai overburdened her with work, and made her perform the work in an intolerably harsh manner. It is even possible that the word ותענה includes physical as well as verbal abuse of Hagar by Sarai. The Torah testifies that Sarai did not act morally and piously toward her. From a moral point of view, although Avram had given her a free hand when he said "do to her as appears fit in your eyes," she should have treated Hagar in a manner befitting her status as a wife or legal companion of Avram. From the point of view of practicing piously, חסידות, she should have treated a subordinate with all possible consideration. The scholar Ibn Gabirol said "how beautiful is the attribute of practicing forgiveness in circumstances when this is possible!" Sarai's actions as reported were not pleasing in the eyes of the Lord. This is reflected in the words of the angel to Hagar (verse 11) כי שמע ה' אל עניך, "for the Lord has listened to the oppression you have endured." This is why the angel gave her a blessing as compensation for the harsh treatment she had suffered. Avram did not prevent Sarai from acting as she did, even though it was displeasing in his eyes, because he was concerned primarily with preserving his relations with Sarai. The reason why this whole story is preserved for all future generations in our chapter is to teach moral-ethical lessons, and to warn us not to indulge in injustice.