Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children;
My understanding is what God wants to express here is that Adam and Eve left the garden of Eden that God is sorrow, because God created life, not death.
Eve's pain in childbirth implies God's sorrow in this matter and the truth that God wants to educate Eve what meaning of life.
and thy desire shall be to thy husband, and he shall rule over thee.
God's purpose may be because Eve listened to the serpent, So God wants Eve to listen to Adam,Because it was Eve, not Adam, who was seduced first.