In the fox hunting scene, I would say the pretty lady represents the Fox. Foxes are very witty and sneaky, the woman demonstrated this behavior as she tries to seduce Gawain while still wedded. This is where (I believe) the lucky number 3 plays in. The fox scene goes along with Lady Bertilak's third encountered. The Fox gets killed and Lady Bertilak's advances towards Gawain fail. In the end, Gawain receives a prize for both accomplishments. From the fox hunt, he has the flesh and fur pelts of the fox, while Gawain receives a green cloth girdle from Lady Bertilak. I believe the significances of those two scene where meant to be character development for Gawain when it comes to honesty and respect, especially with women.
