Genesis 16:5-6 meaning

Sarai considers herself wronged by Hagar and blames the matter on Abram saying, may the wrong done me be upon you. Hagar's pregnancy achieved Sarai's purpose, but the slave's disrespectfulness provoked regret and a cry for help. Sarai directs her anger at Abram. Her view is that Abram had agreed to her suggestion and had caused Hagar's pregnancy, therefore he was responsible. Sarai urges him to deal with Hagar because of her behavior. In other words, Sarai was saying, "I have been wronged and you must answer for it." Sarai's human solution to her barrenness has created new problems. Sarai declared that she wanted the LORD to judge between you and me. She called upon God to hold Abram accountable for her humiliation and pain.

Abram refused to mediate the matter. He removes himself from the conflict by placing Sarai back over Hagar. Although Hagar was now his wife (16:3), Abram puts her back under Sarai's authority saying, behold, your maid is in your power. By traditional custom, Sarai could not sell Hagar as a slave (Deuteronomy 21:14) but could reduce her to servitude once again.  So Sarai treated her harshly.

Sarai's abuse of Hagar caused her to flee from her presence. The pregnant Hagar flees from Sarai, apparently to head toward her country of origin, Egypt. This was a desperate measure because Hagar's survival depended on the protection of a family clan. This would indicate that Sarai's harsh treatment toward Hagar was severe. Sarai apparently does nothing to restrain Hagar from leaving, and her unborn son with her. She no longer seems to have "building" her and Abram's "house" as her primary consideration. It's possible she reasoned that "building up" her and Abram's house by having a son from Hagar was not acceptable if it risked a demotion of her own status. However, God will take up her appeal, and see that the child is born, not in exile, but in the house of Abram.