I’m sure this was asked here multiple times, but I’m having trouble finding it. Can someone please explain to me: 1) how is Adam’s punishment of “eating bread from the sweat of your brow” a rectification of eating from the tree? 2) how is pain in childbirth a rectification for Chava’s part in this?
The punishments are definitely corrective: As I see it, the biggest problem is that Adam cedes responsibility for his one mitzvah to his wife, and even denies responsibility after the fact. He is given a new life which teaches him responsibility: you have to constantly be responsible to work for sustenance. If you shirk responsibility and don't work, you and your family won't eat.
Chava, who was created to be an ezer kenegdo, put herself first and tried to bring Adam down with her. And she used her special influence to bring him down. So now Chava will have pain and struggles with the process of bearing and raising her family which will lead to outward-focused, sacrificial focus on them, AND the balance of power in her relationship with her husband is tweaked so she doesn't have full dangerous control over him. All her punishments are shifting her approach to the main relationships in her life.
The basic answer is that once Adam got the evil inclination, he has to keep it at bay. Therefore he needs to work or else he'll try to do sins.
Regarding Chava it seems from the pirkei drav eliezer ch.21 that it was a natural effect of eating from the tree. The Zohar says people gave birth differently before the eating of the tree.
Maybe say it a little differently. מדה כנגד מדה, each punishment is a consequence of the sin - not necessarily called a "rectification". Adam sinned against the earth that sustained him, by eating a forbidden part. The woman sinned again the man she was created to protect, by leading him into sin instead of being a wall around him against it. The Nachash (highest creature of the Earth) sinned against humanity by leading it astray instead of helping serve Hashem properly.
Thus, each of them were punished by being distanced from their proper service. Adam was supposed to be לעבדה ולשמרה, to work the earth and take care of it; that became harder for him. Chava was supposed to help man populate his world and that became more difficult for her. The Earth was supposed to serve man, and the snake was to be the greatest servant; instead the snake was fired, completely distanced, and the earth could not serve man as well.
Maybe call it grit in the three-part machinery; everything worked same as before, but not properly.