First of all, Scripture states that Jesus Christ offered Himself to God as atonement for our sin (Hebrews 9:14). He laid down His own life on His own accord (John 10:17-18). Mary played no role whatsoever in this act of redemption. Mary could not have offered her son to God as a sacrifice, even if she had wanted to.
Secondly, Mary would have been in agony and distress to see her son nailed to a crucifix. Such reactions are only natural of normal mothers when they see their children suffer. However, there is no valid reason to suggest that Mary's grief had some sort of a unique or redemptive value. She is a human being, not a goddess.