While I hate the Protestants' anti-catholic, anti-Mary "re-interpretation" of Genesis, I always took the crushing of the serpent's head in the garden as Christ, who allowed His human nature to be tempted, decided at that moment to accept His death and reject the weakness of His humanity, as an example to all of us.
As much as it's true that Our Lady will "crush satan's head", we have to remember that Christ's death on the Cross was/is not the end of this prophecy. Christ died, the Church was born, and 2,000 years later, we're still fighting satan. Our Lady's victory is not yet complete.
But in the case of the Garden, and with Christ on the cross, He alone is Our Redeemer. He alone sufficed to God the Father. It is true that it was His victory, alone, who saved us from sin. (Our Lady does play a mystical part in all of this, without question).
But the larger story, post-Crucifixion, post-Resurrection...THAT is when Our Lady took a part in helping the Apostles and praying for the Church. So Her "crushing the head of satan" is ongoing and also, yet to come (God will give Her the final victory).
So, I think both are true. Christ did crush satan's head through His crucifixion, because satan ruled all the world through sin. But Our Lady will also crush satan's head at the end of time, through the Church, as the battle for souls wages on. Our Lady plays a part in both victories, because the story from Eden long ago, is not finished until the end of time.
The prottys always focus on Christ's redemption and think that "the story is over" because "Christ died once and for all", and they believe "once saved, always saved". This is their error. Life goes on, the battle goes on, and Our Lady plays the most important part. Of course, the prottys have no idea about this.