Test the Theory

I would like to try out the Girardian theory on a novel (and I use the term loosely in this case!) that is on my 11th grade summer reading list. It is called Follow the River. 

Two women are escaping Shawnee enslavement. The ordeal makes them turn on one another. This, perhaps, begs some Girardian analysis. Would we say the two idolize each other; and so when the veneer wears off they hate each other? That works; they are both tough and admirable. 

How would such an analysis fir with other kinds of theories -- say a psychological one, where one woman is a "mother figure," and then the escape etc. is about the protagonist reconciling with, or freeing herself from that figure. Or an archetypal analysis, where the old woman represents the alternatively life-giving and death-issuing forces of nature; and then the journey has something to do with the protagonist reconciling herself to that.