Edna decides to leave Earl and return home because she has finally had enough of being with Earl and she sees the kind of rootless, itinerant existence that he leads. She has had enough of living life with somebody that always seems to experience trouble, and Earl is definitely that kind of character. When they reach Rock Springs, it is this that makes their relationships crumble, as Edna is faced with the reality of Earl's life and what her future will look like if she stays with him.
However, it is also important to realise the way in which the ending of their relationship is something that is paralleled by the breakdown of the car that Earl has stolen. There is of course no accident in this. The author is deliberately showing us how everything is breaking down in Earl's life, and as a result, how desperate and broken he is as he contemplates the value of his life. It is this that causes Earl to experience the epiphany at the end of the story where he reflects on life and its value. The ending of his relationship with Edna is a key part of the process that triggers off this epiphany.