The whole of Joyce's Dubliners, first published in 1914, examines how the imperial influences of both the Catholic church and the British have shaped the personal destinies of the Irish. In "Eveline," the inability to throw off those influences leads to a sad, but perhaps inevitable, conclusion.
Eveline's ultimate decision to jilt her fiance and stay with her family, even though it likely means her unhappiness, would be considered the right decision in the eyes of the church and society. In spite of the revolutionary uprising taking shape in 1914 Ireland, religious and social mores' influence—particularly relating to the lives of women—remained firm. A woman abandoning her widowed father and younger siblings would have been looked on unfavorably.
However, the promise of being married would give Eveline a certain standing in society that she had never known. Eveline suggests that her mother and father were not married, and were looked down on for it:
But in her new home, in a distant unknown country, it would not be like that. She would be married--she, Eveline. People would treat her with respect then. She would not be treated like her mother had been.
Here, Joyce highlights that the social status conferred by marriage is the only way a woman could be seen as reputable and respectable, even if she had dutifully raised her children and stayed with their abusive father. Eveline can stay in Dublin and continue to be viewed as a bastard and—eventually, a spinster—or Eveline can flee with Frank, breaking her promise to her mother and potentially bringing further shame to her younger siblings.
Thus, Eveline is truly between a rock and a hard place, both decisions being equally right and equally wrong. One could argue that, in the eyes of the church and in the moralistic post-Victorian era, a woman would not have the luxury of a "right" decision.
Of course, there are opposiing opinions on the decision of "Eveline" in James Joyce's Dubliners. And, the strong influence of the Catholic religion plays a part in Eveline's decision since she has promised her mother, who has died, that she will keep the family together as well as making a promise to Mary that she will do the "proper" thing. This religious aspect is extremely important as Joyce often wrote in reaction to the control that the Church had upon Irish-Catholics. It is no coincidence that Eveline's name resembles Eve, who was also faced with a deeply religious decision.
On the other hand, Eveline realizes that her frail body cannot continue to take the physical abuse of her father. In order to survive, she must leave. But, this departure will leave her little brother vulnerable. Who will intervene for him? Who will cook for him?
With religious connotations again, Eveline reaches what Joyce referred to as an "epiphany." She decides to not sin; she remains true to her promise to her mother and Mary, and she becomes the sacrificial lamb, so to speak.
Thus, the decision comes down to two questions: Does she do what she needs to survive? Or, does she risk scandal by leaving unmarried with a man, breaking her vows to her mother and Mary and deserting her little brother?