Change the narrative style by using indirect speeches :

"Oh, my Lord do not kill the child", said the woman. "Let her have it." The king said, "Now everything is clear to me". Pointing to the woman, he said to the servant, "Give her the child. She is the mother of the child."

Addressing the king as her Lord the woman urged him (king) not to kill the child. Then the king ordered his servant to let her (the woman) have it (child)./She again requested to let her (the other woman) have it (the child). The king again said that everything was clear to him (king) then. Pointing to the woman, he ordered his servant to give her the child and added that she was the mother of the baby.