The Hebrew of Genesis 16:6 is terse, almost stenographic. Targum Pseudo-Jonathan keeps the brevity but sharpens one word: authority.
Behold, thy handmaid is under thy authority, Abraham tells Sarah. Do to her what is right in thine eyes.
Abraham does not mediate. He does not take Hagar's side against his wife, and he does not take Sarah's side against his pregnant concubine. He names the legal fact: Hagar is still inside Sarah's household, still under Sarah's jurisdiction. And he hands the decision back to the woman whose authority he had momentarily interrupted by fathering this child.
What follows is painful. Sarah afflicted Hagar — the verb echoes Sarah's complaint in the previous verse that her honor had been afflicted — and Hagar fled into the wilderness.
The Maggid refuses to pretend this episode is clean. Two women are suffering; a man has stepped back; a pregnant Egyptian is running into the desert; and no one in the tent is going to feel righteous tonight. But the Targum also preserves a principle: Abraham will not protect himself by disrespecting Sarah's standing (Genesis 16:6). The household has an architecture. He may not have managed the situation wisely earlier, but he is not going to compound the error now by pretending Sarah has no say. The Lord, in the next scene, will meet Hagar personally by a spring in the wilderness — because when a human household breaks down, heaven itself will go out looking for the runaway.